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A decentralized control algorithm for routing flow in complex networks is proposed. The aim is to fairly distribute the supply/demand among the nodes while maintaining maximum flow in the network and satisfying the flow limits of the nodes and links. The algorithm is also used for flow re-routing after a failure in (or attack on) a network to avoid a cascading failure while maintaining the maximum flow in the network. The proposed algorithm is based only on the information about the closest neighbours of each node. Consensus rules are used to achieve fairness between the nodes in the network. The performance of the proposed algorithm is demonstrated by simulations. [ABSTRACT FROM AUTHOR]

Russia is the main supplier of fossil energy to European countries. The impact of sanctions on fossil energy trade under the background of the Russia-Ukraine conflict has attracted global attention. Based on the data on fossil energy trade in 2020, this study simulates the impact of sanctions on national trade and global fossil energy trade patterns based on complex network theory and cascading failure model. In terms of negative impact, the crude oil trade has the largest potential impact, the natural gas trade has the largest direct loss and the coal trade has the least impact. To mitigate the impact of sanctions, Russia may shift its fossil-energy export focus to China and other Asian countries. The positive impact analysis shows that crude oil is the main source of benefits for energy exporting countries and the United States will become the biggest beneficiary among energy exporting countries. In addition, the study found that sanctions reshaped the pattern of global fossil energy trade, improved the trade efficiency and energy anti-control ability of European countries, and promoted the transfer of energy control centres from Europe to Asia. It is of great significance to study the impact of sanctions on global fossil energy trade to deal with geopolitical shocks, formulate energy trade policies and manage energy risks. • The sanctions have caused huge direct losses to the gas trade. • The biggest potential impact is on trade in crude oil. • Crude oil is a major source of profit for energy exporters. • The United States will be the biggest beneficiary. • Sanctions promoted the transfer of energy control centers from Europe to Asia. [ABSTRACT FROM AUTHOR]

In the transportation network, we observe that the distance people travel by means of transportation follows a certain distribution. Statistical analysis shows that people's travel distance is mainly concentrated in a medium range by the same vehicle, and they choose fewer destinations that are extremely close or far away. However, in previous studies, the impact of distance on the distribution of load flow within the network has often been neglected, or at best, addressed with overly simplistic assumptions. Therefore, we quantify the load flow distribution based on the Gaussian distribution of distances between the nodes. On this basis, a new cascading failure model is proposed using the shortest path strategy to calculate the initial load of the edge. Through the simulation of three real traffic networks and two artificially constructed networks with similar structural characteristics of traffic networks, we found the following interesting anomalies: First, increasing the load-bearing capacity of edges within the network does not necessarily lead to enhanced robustness. Second, we observed that removing more edges does not necessarily lead to a decrease in network robustness; conversely, the network robustness can be higher when a moderate number of edges are removed compared to fewer edges. To better understand the two anomalous dynamics phenomena we observed, we ran simulations on a small-scale network extracted from a real traffic network. We found that, under certain circumstances, the premature failure of some edges may isolate certain regions from the network, which may be responsible for this paradox. • We quantify the load flow distribution based on the Gaussian distribution. • A new method for measuring initial load on edges is proposed. • We construct a cascading model that considers a load flow mode. • We find abnormal cascading dynamics in transportation networks. [ABSTRACT FROM AUTHOR]

• Design load redistribution methods using network topology and cooperative mechanism. • The cooperative mechanism enhances network resilience by safeguarding critical ports. • The cooperative mechanism reduces shipper losses by balancing carrier and shipper benefits. • Port reserve capacity is crucial for resisting cascading failures in shipping networks. Liner shipping networks play a vital role in global and regional trade. However, they are susceptible to damage from unexpected interruptions, which can trigger dynamic cascading failures and undermine the system's resilience. To address this challenge, we propose a novel cascading failure model for liner shipping networks that considers the characteristics of the network structure and port functions. First, we design two load redistribution methods that rely on network topology and employ a cooperative mechanism for coordination. This cooperative mechanism aims to balance the benefits for carriers and shippers by effectively controlling losses. Subsequently, we develop three metrics—network congestion rate, failure rate, and shipper loss—to assess the resilience of the network during cascading failures. To verify the impact of the cooperative mechanism, we apply the proposed methods to the China-Europe liner shipping network. Through simulations involving various port failures and resistance levels, we analyze the effectiveness of the cooperative mechanism. The results demonstrate that redistributing the load to downstream ports within the network effectively mitigates deep cascading failures. Additionally, the implementation of a port cooperative mechanism enhances resilience in the face of uncertainties by safeguarding crucial ports within the network and significantly reducing shipper losses. When port resistance is low, the cooperative mechanism reduces shipper losses by nearly half and lowers the average congestion rate. Although port reserve capacity can resist cascading failures, it falls short in the face of severe disruptions. In such cases, the cooperative mechanism compensates for capacity shortages, enhancing port resilience at a low cost. This study contributes to combating and minimizing cascading congestion in liner shipping networks, offering valuable insights for risk prevention and management strategies for ports and shipping companies. It also has implications for yield management and policy decisions from a network perspective. [ABSTRACT FROM AUTHOR]

• Presenting an adaptive scheme of estimating the potential of cascading failure as a result of transmission line outages through large power systems. • Developing a set of dominant operating variables to identify cascading failures caused by line outages. • Evaluating the line information consisting of dynamic securities and sensitivities in which the lines with the potential of cascading failures are identified online. • Developing mutual information theory based on the Least Square Error (LSE) method to estimate power system cascading failures without acting any line outages. In this study, the potential of cascading failure as a result of transmission line outages through large power systems is evaluated. Transmission lines are more dispose of the outage resulting from different fault occurrences and extend the uncontrolled failures compared to other power system devices. In this case, power system dynamic security must evaluate the possibility of cascading failures using a power system control center (PSCC) in order to limit the spread of outages caused by line failures. For this issue, using the PSCC online information consisting of power system operating variables, it is possible to present a variables-based scheme to estimate power system cascading failures concerning fault events. In order to cover the issue, based on developing a set of dominant operating variables (DOVs), this paper presents an online scheme of identifying cascading failures caused by line outages in the presence of line operational diversities and communication restrictions. In this scenario, during each time interval, by evaluating the proposed DOVs, the line information consisting of dynamic securities and sensitivities to cascading failure are investigated which the lines with the potential of cascading failures are identified online. Proper DOVs are determined for this issue by studying a variety of mathematical formulations according to theory of mutual information (MI) and measuring the entropy among the variables. In a real-time environment, by using the proposed DOVs and substituting them through online boundary equations based on the Least Square Error (LSE) method, the potentials of power system cascading failures without acting any line outage are provided. The effectiveness of the suggested technique is evaluated using a typical IEEE-39 bus and IEEE-118 bus, and proper results with high accuracy are achieved by evaluating the system potential concerning large cascading failures. [ABSTRACT FROM AUTHOR]

Cascading failures can be triggered within the closely interconnected Integrated Electric and Gas System (IEGS) due to the propagation of failures from either the power or gas system through their coupling components. Traditional cascading failure analyses typically involve time-domain modeling of the gas system, which is computationally complex and hinders the rapid study of failure propagation between subsystems. To address this issue, this paper proposes a novel cascading failure model of IEGS integrating a dynamic gas system model based on energy circuit (EC) in the frequency domain and a power system model based on steady-state DC in the time domain. First, considering the variable flow velocity of pipelines before and after a failure, a data fusion method for dynamic flow with multiple sets of flow velocity base values (FVBV) is proposed. Then, by modifying the original gaseous circuit matrix, the new network equations for the branch containing fixed-mass-flow-rate compressors are derived. Finally, a co-simulation approach for cascading failure analysis, featuring alternating flow calculations throughout the temporal domain, is established to investigate the propagation process of failures. Compared with the Finite Differential Method (FDM), numerical results demonstrate that computational efficiency is enhanced by over 10 times with the proposed method while meeting the required precision. • The proposed model for studying cascading failure can enhance calculation efficiency by over 10 times compared with the traditional model. • Introducing a dynamic gas flow data fusion method with multiple sets of flow velocity base values aims to enhance computational accuracy. • The new gas network equation includes a more refined compressor model achieved by modifying the original gaseous circuit matrix. • A cascading failure co-simulation framework based on energy circuit is established to capture the dynamic behavior of failure propagation. • An iteration method for mass flow rate is adopted to precisely calculate the energy transfer through the compressor. [ABSTRACT FROM AUTHOR]

Cascading failures are ubiquitous in physical networks such as power grids and water networks and have become a trending research topic in the field of complex networks. In real cases, once a node in a network fails, the entire system can completely collapse, causing considerable economic losses and casualties. Implementing an appropriate node repair strategy can effectively prevent system crashes in complex networks due to cascading failure. This paper presents a network cascading failure propagation model with a node emergency recovery function. Numerical simulations with typical case scenarios are conducted to analyze network cascading failure when the nodes have an emergency recovery probability. The results of the case study show that incorporating an emergency recovery probability for nodes can reduce the maximum failure probability of nodes in a network and reduce the risk of network failure. As the recovery probability increases, the network failure risk probability gradually decreases. The proposed network cascading failure propagation model with a node emergency recovery function can accurately reflect the dynamic behavior of complex network cascades and provide a reference for the control and prevention of cascading failures in actual networks. • Propose a network cascading failure propagation model with a node emergency recovery function. • Numerical simulations are conducted to analyze the network cascading failure phenomenon with different recovery probability. • Considering two cascading failure modes, the initial failure mode, and the coexistence of initial and progressive failures. [ABSTRACT FROM AUTHOR]

Power grids are susceptible to cascading failure, which can have detrimental consequences for modern society. Remedial actions, such as proactive islanding, generator tripping, and load shedding, offer viable solutions to mitigate cascading failure in power grids. The success of applying these solutions lies in the timeliness and the appropriate choice of actions during the rapid propagation process of cascading failure. In this paper, we introduce an intelligent method that leverages deep reinforcement learning to generate adequate remedial actions in real time. A simulation model of cascading failure is first presented, which combines power flow distribution and the probabilistic failure mechanisms of components to accurately describe the dynamic cascading failure process. Based on this model, a Markov decision process is formulated to address the problem of deciding on the remedial actions as the failure propagates. Proximal Policy Optimization algorithm is then adapted for the training of underlying policies. Experiments are conducted on representative power test cases. Results demonstrate the out-performance of trained policy over benchmarks in both power preservation and decision times, thereby verifying its advantages in mitigating cascading failure in power grids. • A Markov decision process is formulated to determine real-time remedial action scheme (RAS) for mitigating cascading failure in power systems. • A proximal policy optimization (PPO) adaptation is developed for the training of RAS policies offline. • Numerical studies are performed based on cascading failure simulations in IEEE 39-bus and 57-bus systems. • The PPO-based RAS can effectively slow down or inhibit the propagation of cascading failure. [ABSTRACT FROM AUTHOR]

The frequent occurrence of ice disasters, such as blizzards and freezing rain, poses significant challenges to the safe operation of electric-thermal energy networks. This paper proposes a resilience assessment method for electric-thermal energy networks that accounts for fault propagation. Initially, a line fragility model is established considering icing failures and overload failures under ice disasters. Integrating the fault propagation mechanism, a cascading failure graph of electric-thermal energy networks is proposed, grounded in complex network theory. Furthermore, a resilience index scheme encompassing both component and system levels is constructed. To address the impact of cascading failures on electric-thermal energy networks amid prolonged ice disasters, a strengthened distributionally robust resilience assessment numerical model is formulated, taking into account the uncertainty of wind power. Different scale test systems and an actual energy networks are conducted to validate the scalability and the practicality of the propose method, accurately identifying critical vulnerabilities and quantifying the resilience of electric-thermal energy networks. • A cascading failure graph based on complex networks theory is proposed. • A resilience index scheme encompassing both component and system levels is constructed. • Taking into account the uncertainty of wind power, a strengthened distributionally robust resilience assessment numerical model is formulated. • The impact of different improvements on the resilience of electric-thermal energy networks is thoroughly investigated. [ABSTRACT FROM AUTHOR]

• A novel cascading model for the global container shipping network is proposed. • Cascading failure diffusion process are showed using mass vessel trajectory data. • Significance similarity of failure ports through the process of relevance mining. Port plays a key role in maintaining traffic flows and the effectiveness of global maritime logistics. However, the vulnerability of the Global Container Shipping Network (GCSN) is likely to increase when a single port interruption entails failures in cascading when ports encounter situations like congestions, labor strikes or natural disasters. Such situations require the deployment of port protection measures and adjustments of shipping schedules. This paper introduces a cascading model, which employs extensive and worldwide vessel trajectory data to comprehensively analyze the occurrence of cascading failures within a GCSN. The principles behind the cascading failure model are that port failures are simulated and the maritime traffic is redistributed and equilibrated to other routes and ports. A Motter-Lai overload model is applied, complemented by a three-level balanced redistribution of the traffic flows according to the specific roles of the disrupted ports. Overall, this favors the analysis of the GCSN's vulnerability, reliability, potential risks, and possible impacts. It enables maritime authorities and decision-makers to optimize service routes and mitigate the GCSN's vulnerability. [ABSTRACT FROM AUTHOR]

The critical infrastructure system exhibits a high degree of instability because of the frequent occurrence of extreme natural disasters. This study proposes a method for exploring the cascading failures of critical infrastructure systems under such impacts, based on dependency relationships for importance analysis and probability assessment. With this method, a cascading failure scenario graph of critical infrastructure is established and empirical research is conducted using typhoon rainfall events as a case study. The main contributions of this study are summarized as follows: it proposes a method for the causal identification of the interrelationships among critical infrastructures; it sorts and evaluates the importance and cascading failure probability of critical infrastructure by using the Interpretative Structural Modeling (ISM) and Rank-order Centroid method (ROC); and it generates scenario graphs of critical infrastructure cascading failures to visualize event states, environmental characteristics, and evolutionary paths. This study provides a new method and tool for disaster risk management of complex systems involved in critical infrastructure. [ABSTRACT FROM AUTHOR]

A significant amount of society's infrastructure can be modeled using graph structures, from electric and communication grids, to traffic networks, to social networks. Each of these domains are also susceptible to unwanted cascades, whether this be overloaded devices in the power grid or the reach of a social media post containing misinformation. The potential harm of a cascade is compounded when considering a malicious attack by an adversary that is intended to maximize the cascade impact. However, by exploiting knowledge of the cascading dynamics, targets with the largest cascading impact can be preemptively prioritized for defense, and the damage an adversary can inflict can be mitigated. While game theory provides tools for finding an optimal preemptive defense strategy, existing methods struggle to scale to the context of large graph environments because of the combinatorial explosion of possible actions with the size of the graph. Data-driven deep learning approaches can fill this gap, but they demand a large amount of data that is often costly to obtain. We propose a novel data generation approach for the cascading failure security problem that uses counterfactual data augmentation and a sub-game data querying strategy to generate both high quality and a high quantity of training data. We demonstrate that our data generation approach creates up to an order of magnitude more data than naïve querying with double the efficiency. We also introduce a deep learning model based embedding node pairs, and train it on our generated data, showing that it effectively defends from cascades on graphs as large as 1000 nodes. Our deep learning approach achieves a closer approximation to the Nash Equilibrium than existing heuristic methods, for graphs where the ground-truth equilibrium can be calculated. • Efficient counterfactual data generation for cascading events. • Machine learning for game theoretic defense from cascading failure. • Competitive influence maximization in large scale graphs. [ABSTRACT FROM AUTHOR]

• Reliability of URTNs considering the traffic congestion diffusion is studied. • An improved NLC model under different attack strategies is proposed to simulate cascading failures. • A load redistribution method with the impedance function is provided. • Formation time, diffusion speed, and scale of cascading failures are analyzed. The cascading failures caused by traffic congestion diffusion may deteriorate traffic network reliability. Comprehending urban traffic congestion mechanisms is essential for road network planning and traffic management against cascading failures. To uncover this, the reliability of urban road traffic network (URTN) under cascading failure considering different attack strategies is analyzed. The cascading failure model is established based on the improved nonlinear load-capacity relationship. Five kinds of attack strategies including Strength Attack (SA), Betweenness Centrality Attack (BCA), Eigenvector Centrality Attack (ECA), Closeness Centrality Attack (CCA), and Random Attack (RA) are selected. In particular, the capacity affected by traffic congestion is considered, providing a new perspective for the study of traffic congestion diffusion. A state update equation for networks is proposed to simulate the network congestion diffusion. Finally, a case study is conducted by using the URTN of Shanghai as the background. The results show that the network will experience large-scale congestion when high-importance nodes are attacked. The congestion degree is the highest under CCA strategy, network efficiency is the lowest under ECA strategy, and traffic quality is the poorest under CCA strategy. As the congestion critical failure threshold decreases, the speed and scale of cascading failures caused by traffic congestion diffusion are greater. Maintaining proper traffic management and control capability can largely reduce the cascading effect to a great extent and improve the reliability of the network. The results can provide a research basis for traffic management to improve network reliability. [ABSTRACT FROM AUTHOR]

• Construction of more realistic physical and cyber models based on the probabilistic line outage rule and an improved cyber flow approach. • Development of a coupling layer model for the CPS by sorting the nodes based on their impact on system load shedding and network efficiency after failure. • Introduction of a multi-stage attack strategy, i.e., N-k , to simulate low probability high-risk events in CPS, differing from the traditional N-1 and N-2 approaches. • Consideration of interdependency probabilities during the analysis of system robustness by considering the presence of backup power sources for the cyber layer. This includes the probability of cyber node failures caused by physical node failures. Evaluating the robustness of cyber-physical system (CPS) under multi-stage attacks is fundamental to enhancing CPS resilience. Currently, many models inadequately consider information flow, which is not aligned with reality. The initial focus of this paper is on introducing a weakly coupled interdependent model for CPS. This model considers probabilistic line outage rules, cyber flow transmission characteristics, and the probabilities of inter-system coupling failures. Subsequently, the multi-stage attack strategies are presented and employed by the proposed model during disaster scenarios, along with the proposed robustness assessment indicators. The numerical results illustrate the robustness of the weakly-coupled CPS model under multi-stage attacks. This lays a modeling and simulation foundation for repair crew to enhance the CPS resilience. [ABSTRACT FROM AUTHOR]

• Analyze the cascading failure for different situations in distribution networks. • Improve the reliability and shorten the cascade failure time by two shunt methods. • Increase network resilience by adding unmanned vehicle delivery tasks. • Propose a time-varying resilience optimization algorithm. • Provide three resilience optimization strategies for distribution networks. With the development of science and technology, unmanned vehicles have become one of the main ways of distribution, and the appearance of unmanned vehicles undoubtedly brings great convenience to people. However, few researchers consider the cascading failure times for different situations in unmanned vehicle distribution networks. Especially, few researchers have integrated them into maintenance strategies to real-time path changes to increase the reliability of accomplishing distribution tasks and improve resilience after congestion. One of the key issues is how to improve the resilience of distribution network and what maintenance strategies should be developed. In this paper, cascading failures are analyzed and resilience is optimized in unmanned vehicle distribution network. First, cascading failures for different situations are analyzed, and two importance-based diversion methods are proposed to describe the three processes of congestion formation, persistence, and evacuation. Second, failure and performance degradation processes are investigated. Third, the Floyd time-varying resilience optimization algorithm is proposed, and the calculation method of resilience under different strategies is given. At last, simulation results show that the proposed strategy 3 improves the original resilience by 101 % compared with the traditional waiting path strategy. [ABSTRACT FROM AUTHOR]

The cascading failure of multiple landslide dams can trigger a larger peak flood discharge than that caused by a single dam failure. Therefore, for an accurate numerical simulation, it is essential to elucidate the primary factors affecting the peak discharge of the flood caused by a cascading failure, which is the purpose of the current study. First, flume experiments were done on the cascading failure of two landslide dams under different upstream dam heights, downstream dam heights, and initial downstream reservoir water volumes. Then, the experimental results were reproduced using a numerical simulation model representing landslide dam erosion resulting from overtopping flow. Finally, the factors influencing the peak flood discharge caused by the cascading failure were analyzed using the numerical simulation model. Experimental results indicated that the inflow discharge into the downstream dam at the time when the downstream dam height began to rapidly erode was the main factor responsible for a cascading failure generating a larger peak flood discharge than that generated by a single dam failure. Furthermore, the results of a sensitivity analysis suggested that the upstream and downstream dam heights, initial water volume in the reservoir of the downstream dam, upstream and downstream dam crest lengths, and distance between two dams were among the most important factors in predicting the flood discharge caused by the cascading failure of multiple landslide dams. [ABSTRACT FROM AUTHOR]

The 21st-century Maritime Silk Road container shipping network (MSRCSN) is pivotal for global economic and social progress, yet it exhibits vulnerabilities impacting the stability of maritime transportation and international trade. This study conducts a comprehensive analysis of the MSRCSN's network topology, demonstrating its insignificant small-world and scale-free properties. We introduce an enhanced cascading failure model grounded in a nonlinear capacity framework, enabling the examination of maritime shipping networks' vulnerability to cascading failures, predicated solely on routes connectivity and empirical port load data. Applying this model to the MSRCSN, our findings corroborate a pronounced increase in dynamic vulnerability due to cascading failures, compared to static vulnerability. The network's static structure is exceedingly susceptible to disruptions at ports with high connectivity, whereas in the context of cascading failures, the greatest vulnerability lies in ports with substantial load. Efforts to augment port capacity yield marginal benefits in mitigating dynamic vulnerability. We propose the novel concept of network capacity investment cost, revealing that prioritizing capacity redundancy for lower-load ports can optimize overall investment efficiency in network capacity. These insights offer strategic guidance for enhancing the resilience of the MSRCSN against vulnerabilities. [ABSTRACT FROM AUTHOR]

• An efficient nonlinear method is proposed for cascading failure analysis. • The impact of overturning angle on cascading failure is investigated. • The PCCC is developed to optimize structural parameters of a PDL. The weakest poles in a power distribution line (PDL) will overturn first and then cause additional impacts on adjacent poles through wires, which may trigger catastrophic cascading failures. This paper aims to develop a more accurate and efficient approach to support risk assessment of cascading failures for PDLs under wind hazards. The failure propagation equation is first proposed, which is a nonlinear method for solving tensions of a multi-span PDL considering the pulling effect of failed poles; The vertical and horizontal overturning angles of failed poles are determined, and their impact on cascading failures is investigated. Regarding the cascading effect, the structural fragility is estimated using Monte Carlo method, and the failure probability is further obtained considering the joint distribution of wind speed and direction. Finally, an innovative probability-based critical collapse curve, featured by optimizing structural parameters including horizontal span and operating tension, is proposed to reduce cascading failure risks. Compared with previous works, the proposed method exhibits unique advantages in terms of accuracy; Ignoring the influence of overturning angle overestimates additional tensions; The failure probability significantly increases after considering the cascading effect. The proposed method possesses extensive application prospects in performance evaluation and anti-continuous collapse design of PDLs. [ABSTRACT FROM AUTHOR]

The identification and protection of critical nodes have a significant influence on the reliability and robustness of the cyber–physical power system (CPPS), which can effectively reduce the risk of cascading failures. Firstly, this paper establishes a one-to-one coupled cascading fault model, which considers different topological characteristics of power and cyber networks. Based on the interdependence between the two networks, the cascading fault propagation mechanism after node failures in CPPS is analyzed. Then, a critical node identification method based on improved adaptive differential evolution (JADE) is proposed to identify the sets of critical nodes that can maximize the impact on the system load of CPPS. Combined with the cascading failure characteristics of CPPS, in the population generation strategy, the test vectors that do not meet the conditions after the crossover operation are filtered and replaced to improve the search efficiency of the algorithm. Finally, in the case study, an interdependent CPPS is constructed with an IEEE 39-bus system and a scale-free network of the same nodes. The simulation results verify the effectiveness of the proposed node importance assessment strategy. In addition, it is also shown that evaluating the critical nodes in power systems is important for enhancing the robustness and ensuring the security of the power grid operation. • An improved JADE method is proposed to identify the sets of critical nodes in CPPS. • By adopting the identification method of JADE, the sets of critical nodes with a greater impact on the system load can be obtained. • The specific solution representation and the population generation technique of power systems are introduced into the improved JADE method to effectively solve the IM problem of CPPS. • The established cascading failure model provides a feasible way to analyze the propagation mechanism after node failure in CPPS. [ABSTRACT FROM AUTHOR]

Land system face multiple threats due to the long-term effects of climate change, global geopolitical and economic. Our research simulates the static and dynamic resilience of land systems under increasing socioeconomic pressures and frequent disturbances from natural disasters. We use an improved load-capacity model to simulate the cascading failure effects of agricultural land systems. The study finds that parameters change after deliberate attacks much earlier than random attacks that cause network collapse. The core nodes in the trade structure carry most of the functions, and such regions and land types should be focused on. Cascading failures make the network more vulnerable due to the transmissibility of pressure. Static attacks can cause network collapse when more than 30% of nodes are attacked, while dynamic attacks only need to attack 10% of nodes. According to parameter optimization, the node capacity should be maximized while reducing the gap in the initial load of the nodes, thereby weakening the cascading effect. To ensure the reliability of the results, the article conduct robustness tests. Finally, in order to develop sustainable land systems, the article propose that it is necessary to assess resilience, identify key elements, effectively monitor land systems, and develop sound land protection plans. [ABSTRACT FROM AUTHOR]

Drawing on complex network theory, this paper combines bus network and subway network into a multi-subnet composited complex network (MSCCN) of urban public transport (UPT). Then, the cascading failure of the MSCCN nodes and edges was modelled, and the passenger flow transfer rules were established under node and edge failures. Considering the impact of extreme weather on the UPT, a synthetic operator was created to measure the robustness of UPT MSCCN, in the light of network topology and passenger flow, and used to quantify the robustness of UPT MSCCN under extreme weather. Finally, a UPT MSCCN was set up for Qingdao, China, and subject to cascading failure simulation. The simulation results reveal how MSCCN robustness changes with different variables. The research findings help to optimize the response of the MSCCN to extreme weather. [ABSTRACT FROM AUTHOR]

• Propose a model predictive approach to protect power grids against cascading blackouts. • Establish a nonlinear convex optimization formulation to characterize the optimal load shedding. • Design two protection schemes on the basis of the optimization formulation. Large scale blackouts normally go through several sequential phases according to the propagation speed of branch outages and the disruption level of power grids. It is crucial to eliminate the propagation of cascading outages in its infancy. In this paper, a model predictive approach is proposed to protect power grids against cascading blackouts. First of all, the cascading dynamics of power grids is described by the outage model of transmission lines and the DC power flow equation, which allows us to predict the cascading failure path. Then a nonlinear convex optimization formulation is established to terminate the cascading outages by adjusting the injected power on buses. Afterwards two protection schemes are designed according to the optimization formulation: one scheme carries out protective actions to terminate cascading outages once for all, while the other takes protection measures in two consecutive steps. Saddle point dynamics is employed to provide a numerical solution to the proposed optimization problem, and its global convergence is guaranteed in theory. Finally, numerical simulations on IEEE test systems are implemented to validate the proposed approach. [ABSTRACT FROM AUTHOR]

Cyber attacks from the information layer can have a serious impact on the operation of the cyber-coupled power system. In this paper, a practical cascading failure model used for investigating the impact of virus propagation on the cascading failure of cyber-coupled power system is proposed. The model takes into account the actual functionality of cyber-coupled system and the dynamic virus propagation in cyber network, and describes the effects of cyber node failure caused by virus infection and power flow overload on the cascading failure. Moreover, the impact of defense upgrade on the virus propagation is considered. Centralized control based on dispatching center and local regulation based on static power-frequency characteristic are introduced to describe the actual monitoring function of cyber system on the power grid. Then, the effects of defense upgrade strategy and modular community structure on the failure evolution are analyzed. The results indicate that the spread of virus destroys the monitoring function of cyber network on the power network and leads to more serious failure results. The effectiveness of defense upgrade strategies is related to the upgrade probability of information stations. In addition, the stronger community structure of cyber network can improve the robustness of cyber-coupled power system. • A cascading failure model of cyber-coupled power system considering virus propagation is proposed. • A virus propagation model that takes into account network defense upgrade is proposed. • The impact of defense upgrade strategy on the cascading failure of coupled system is investigated. • The impact of modular community structure on the robustness of cyber-coupled system is analyzed. [ABSTRACT FROM AUTHOR]

The critical to sustainable urban development that a robust bus transit system is constructed to alleviate urban congestion problems. Unfortunately, disruptions in bus transit systems can lead to dysfunction and threaten sustainable development. This paper proposed a vulnerability analysis model for constructing complementary urban bus networks (UBNs), which considers the actual capacity of the bus network at the speed of transport roads. In addition, the UBNs aimed analysis method is presented from three specific aspects: (a) utilizing the stochastic user equilibrium model and different traffic situations to measure the UBNs of passenger flow distribution according to multi-source data; (b) introducing the node capacity and structural, functional vulnerability analysis model by combining real traffic flows and the complex network theory; (c) analysing the vulnerability characteristics of UBNs cascading failures from different passenger flow distributions and increasing capacity parameters, and comparing with those under different attack methods. Then, the new vulnerability analysis model is applied to the Harbin trunk bus. Considering different attack scenarios, the UBNs show strong vulnerability in the case of high congestion. Compared with other deliberate attacks, the bus network based on the attack mode of the maximum intensity site is more vulnerable at different times. These insights could be used to inform a vulnerability-based spatiotemporal design of bus transit networks. • An urban weighted transit network model is developed using multivariate data. • Network vulnerability based on traffic situation is proposed. • The network shows significantly varied vulnerability behaviors throughout the operation. • The temporal estimation of the network vulnerability is more effective than traditional weighted networks. [ABSTRACT FROM AUTHOR]

• A novel Coordinated Cyber-Physical Attacking (CCPA) mode on power grids. • Full malicious power dispatch based on false command injection by maximizing inverse-community characteristic as objective to quantify vulnerability of the system. • Partial malicious power dispatch as the measure in CCPA. • Demonstration of the proposed novel CCPA mode. This paper proposes a new mode of cyber-physical attack based on injecting false commands, which poses an increasing risk to modern power systems as a typical example of Cyber-Physical Systems (CPS). Such attacks can trigger physical attacks by driving the system into vulnerable states. To address the critical issues arising from this new mode, we define an inverse-community (IC) in power flow distribution and evaluate it using inverse-modularity. To identify the most vulnerable state of the IC that represents the inherent vulnerability of the system, we employ a full malicious power dispatch problem. We also analyze an example of the proposed mode, where a partial malicious power dispatch that maximizes inverse-modularity is combined with physical attacks aimed at disconnecting vulnerable IC boundary lines, making cascading failures highly likely. To demonstrate the potential impact of this coordinated cyber-physical attack, we use the IEEE-118 and IEEE-300 bus systems for simulation. The results show the effectiveness of this attack strategy and provide a new perspective to analyze cyber-physical security issues in modern power systems. [ABSTRACT FROM AUTHOR]

The resilience of ecological networks is an important guarantee for maintaining regional ecological stability. However, current research on the resilience of ecological networks does not take into account the dynamic processes of the network. This study is based on complex network theory, takes the southern foothills of the Qilian Mountains in China as the research area, and uses the shortest path method to construct an ecological network with 104 nodes and 306 edges. It then uses the cascading failure model to simulate the dynamic response process of the ecological network under different attack strategies, and uses this to evaluate the resilience of the complex ecological space. The research results show that The topological structure of the ecological space network in the southern foothills of the Qilian Mountains has the characteristics of fewer central high-degree nodes and more peripheral low-degree nodes; When the initial load intensity difference of each ecological node in the network is small, the attacked low-degree nodes make the decline in network resilience more obvious. When the initial load intensity difference of each ecological node in the network is large, the attacked high degree nodes make the decline in network resilience more obvious. The study suggests that maintaining the load of high degree nodes and increasing the capacity of low degree nodes are the keys to maintaining network stability. The results provide a new perspective for optimising ecological network configuration and protecting key areas. [Display omitted] • Simulate the dynamic process of ecological spatial networks under attack. • When α < 1, attacking low-degree nodes causes more severe consequences. • The model reflects the intrinsic link between network topology and cascading failures. [ABSTRACT FROM AUTHOR]

• Failure of major drainage systems manifests as waterlogging. • Application of cascade failure theory and model in mountain hydrology. • Potential waterlogging locations far outweigh the current situation. • The terrain will dominate the pattern of cascading failure of major drainage systems. • Provide a basis for the prevention and control of waterlogging in mountainous cities. Failure of major drainage systems is almost always accompanied by waterlogging. Understanding the operation and failure mechanism of major drainage systems is an important prerequisite for understanding and managing waterlogging. The natural and artificial environments in mountainous cities are more complex, and the major drainage system, as an open system for excessive surface runoff discharge and storage, is more prone to local overload and cascading failure. Existing theories and methods are difficult to explain and analyze the cascading failure characteristics and principles of major drainage systems in mountainous cities. Based on the complex network technology and the principle of runoff balance, the cascade failure model of major drainage system was constructed, and the characteristics and laws of cascade failure under six kinds of terrain, six kinds of short duration rainstorm and two kinds of surface environments were quantitatively analyzed. Research has found that the cascading failure of major drainage systems and waterlogging in mountainous cities should be the same phenomenon from different perspectives, and the simulated matching degree between the two can reach 79.5%. Meanwhile, 456 potential waterlogging locations were discovered in the study area, which is much larger than the actual 73 locations. When urban construction and rainfall conditions change, these unstable potential waterlogging locations are easily apparent. Among them, terrain is the main factor restricting the cascading failure of major drainage systems. Low lying valley areas often quickly accumulate a large amount of overflow, while flat areas are prone to overflow spreading to the surrounding areas; Slope areas are not prone to overflow, but are prone to local flooding. The change of short duration rainstorm and the difference of surface environmental openness will further interfere with the cascade failure of the major drainage system. The longer the return period of the short duration rainstorm or the increase of the peak value of the rainfall pattern, the greater the discharge and storage pressure of the major drainage system per unit time, resulting in intensified waterlogging. The open and unobstructed surface environment will lead to the small-scale spread of waterlogging, but this will significantly reduce the overall degree of waterlogging in the late rainstorm. The study revealed the spatiotemporal principles and basic laws of cascading failure of major drainage systems in mountainous cities. The conclusion is helpful for mountainous cities to formulate urban construction management strategies and climate change adaptation strategies, and to cope with current and future potential waterlogging disasters. [ABSTRACT FROM AUTHOR]

The identification of critical nodes is important for safe operation and accident prevention in power grids. With the accelerated development of renewable energies, the uncertainty of renewable energy has brought greater challenges to the node importance assessment of the power system. The electrical spreading probability method is proposed in this paper to identify the critical nodes in the power grid containing renewable energy. First, the uncertainty factors of renewable energy are established through probability density functions, and Monte Carlo simulation and stochastic DC optimum power flow are adopted to effectively deal with the impact of uncertain power output from solar and wind energies. Then, considering the system topology and load loss after cascading failures calculated by Monte Carlo simulation, a method is proposed to calculate the probability of nodes being infected. Finally, according to the Susceptible–Infected model, a method depending on the propagation ability of nodes is proposed to identify the critical nodes in the complex power system. The effectiveness of the proposed ESP method is verified through simulation examples of the modified IEEE39 power system and the modified IEEE118 power system. • An electrical spreading probability method is proposed. • By adopting the ESP method, a more accurate assessment result can be obtained. • More effectively eliminate the uncertainty brought by renewable energy integration. [ABSTRACT FROM AUTHOR]

Cascading failure in interdependent networks is studied in recent decade, and considerable research has been done on systems modeling, vulnerability analysis and protection strategy, but partial work on vulnerability analysis and protection strategy still cannot completely utilize coupling relation between physical power grid and communication network into research, thus we introduce inter-relation of support nodes to perfect the strategies. Compared with traditional vulnerability analysis, we, through studying state of systems after attack, analyze robustness of systems. From the perspective of attacker, four attack strategies considering inter-relation have been proposed, and simulation results verify the serious destructiveness of attack strategies to steady of systems. Taking inter-relation and heterogeneity of networks into consideration, we propose two redundancy protection strategies on intra-links redundancy. Both protection strategies are proved to attain better performance than other strategies without considering inter-relation, meanwhile existence of saturation point can give guidance on rational allocation of limited intra-links. • Four optimizing attack strategies are proposed to detect critical nodes. • Cascading failure is simulated in four coupled symmetric networks. • Two optimizing intra-links addition strategies are raised. • The effectiveness of optimizing attack and intra-links addition strategies. • Discovery of saturation point has guide in rationally allocating limited resource. [ABSTRACT FROM AUTHOR]

Abstract Considering that network community might have a profound effect on the cascading failure of R&D network, we generate the weighted scale-free R&D network and quantify the network community through network modularity Q. Afterwards, we propose the cascading failure model of R&D network based on SIR-CA model, and analyze the special effects on the cascading failure of R&D network through numerical simulation. The simulation results show that network modularity Q has a U-shaped effect on the robustness of R&D network, there is a negative correlation between the delay effect and the robustness of R&D network. Additionally, we verify that overlapping firms have more significant influence than those firms with the same degree and K-shell on the robustness of R&D network. This paper reveals the law of cascading failure of R&D network considering the network community, which is of practical significance to enhance the robustness of R&D network, and enrich the theory of dynamics of the network community. Highlights • The cascading failure model of R&D network based on the SIR-CA model. • The impact of community structure on the cascading failure of R&D network. • The effect of the delay effect on the cascading failure of R&D network. • The effect of overlapping firms on the cascading failure of R&D network. [ABSTRACT FROM AUTHOR]

Highlights • A stability analysis method is proposed in consideration of fault intervals. • The proposed method chooses the most unstable interval. • The method captures the periodicity of stable margin variations with intervals. • The mechanism of the periodicity is analyzed in consideration of time-varying factors. • The proposed method is compared with common assumptions in cascading failure TSA. Abstract Cascading failure analyses are mainly based on simultaneous or quasi-steady-state (QSS) assumptions, which are inappropriate in cases of rapid cascading failure analysis and control. Fault interval is considered in the stability analysis of cascading failure for the first time in this article. Based on the extended equal area criterion (EEAC), a transient stability analysis method is proposed for cascading failure in consideration of intervals. The results show the periodicity of stable margin variations with intervals. The conclusions are validated in a Hamiltonian system, and the effects of time-varying factors are analyzed. The OMIB case shows that it may be over-optimistic to assess stability levels under simultaneous or QSS assumptions. The validity of all conclusions in this paper is verified with the New England system and with an actual power system. [ABSTRACT FROM AUTHOR]

Abstract Many networks are physically or logically interdependent with each other, such as smart power grid, city traffic network and communication systems, where cascading overload failure becomes a major threat. Based on a load-dependent cascading model, we investigate the restoration characteristics in the consideration of repair resource, timing and load tolerance, for different coupling strength and network topologies in interdependent networks. We find that the restoration on the network with different coupling strength may lead to two extreme system effects with early repair: full recovery or completely collapse. Furthermore, SF–SF network is sensitive to repair resources, while repair effect of ER–ER network increases sharply when load tolerance is increased. When overloads are triggered in an ER network coupled with a SF network, the restoration effect can be obviously worse than other topology combinations. Our findings may help to design restoration strategy for interdependent networks and improve the system resilience. Highlights • Repair effect of interdependent network becomes worse with the increasing coupling strength. • SF–SF network is sensitive to repair resources while ER–ER network is sensitive to load tolerance. • ER–SF network exhibits worse repair effect than ER–ER, SF–SF, and SF–ER network. [ABSTRACT FROM AUTHOR]

Cascading failure is an ubiquitous phenomenon in many types of complex networks, and it has attracted significant concerns in the past decade. In this paper, we consider a generic transmission network consisting of two kinds of nodes, i.e., hosts and routers, and only the hosts can generate and receive packets. In such a host–router network model, the network robustness against cascading failure is closely related to the hosts’ locations. We employ the memetic algorithm (MA) to find a near-optimal way to locate the hosts, which remarkably improves the network robustness compared with three degree-based methods. Furthermore, we investigate the optimal configuration of the hosts given by the MA algorithm and put forward a faster method to select the hosts. This work provides a start point for systematically analyzing and optimizing network robustness of complex networks with heterogeneous node functions. [ABSTRACT FROM AUTHOR]

The memory effect of node fragility plays an important role in determining the cascading dynamics of complex systems. This paper focuses on the impact of non-Markovian characteristics of cascading dynamics on system robustness, where the fragility of each node evolves with the increase of failed neighbors and governs the failure probability of the node. The research reveals that the rate of change in node fragility not only impacts the critical point of the system's phase transition but also influences the manner in which the system collapses. Notably, the collapse patterns of the system can exhibit first-order, second-order, or double-phase transitions. Additionally, the initial fragility of nodes has a great impact on the occurrence of cascading failures. Specifically, when the initial fragility of nodes exceeds the inverse of the mean degree, the network experiences an abrupt collapse even with the removal of an infinitesimally small fraction of nodes, regardless of memory effects. The findings provide profound insights into the intricate interplay between dependent relationships and memory effects during cascading failure processes. Furthermore, it offers a deep understanding for effectively assessing the vulnerability of complex systems and devising strategies to mitigate cascading failures. • We analyze memory effects in random networks, where nodes' fragility changes. • The change rate in node fragility affects percolation transition and system collapse. • As initial fragility exceeds inverse of mean degree, networks abruptly collapse. [ABSTRACT FROM AUTHOR]

[Display omitted] • A network modeling framework suitable for various types of heterogeneous risk factors in urban floods has been proposed. • Simulation of the cascading effects of heterogeneous hazard-bearing bodies in the city from a functional availability perspective under continuous flood attack. • The heterogeneous hazard-bearing bodies are interdependent and networked, which causes flood damage to spread more quickly and widely. • The greater degree and more propagating hazard-bearing bodies are key factors influencing the spread of flood risk and the cascading failure of functionalities in urban areas. Increasing urban flooding posed serious threat to urban safety and sustainable development. The heterogeneity of hazard-bearing bodies is one of the important reasons for the variability of cascading failure scenarios in floods. Most previous studies have focused on failure propagation risks among specific types of hazard-bearing bodies, making it impossible to conduct a systematic analysis of the damage caused by persistent flooding in cities. In contrast to conventional graph representations, the heterogeneous hazard-bearing bodies network (HHBBN) based on heterogeneous functional graph theory was constructed in this paper and used to capture the relevant associations of urban resources in a flood. The HHBBN takes into account heterogeneity such as sensitivity and service diffusivity, and functionalities related to hazard-bearing bodies are represented as nodes, with service relationships and geographical associations depicted as edges. To further study the performance change of HHBBN in urban areas during rainstorm flooding, the cascading failure of HHBBN under continuous disturbance was also simulated. The proposed network modeling and cascading failure simulation methods were tested in Futian District of Shenzhen City, China. The case results demonstrate that the heterogeneous hazard-bearing bodies are interdependent and networked, which causes flood damage to spread more quickly and widely. Furthermore, the larger degree and more propagating hazard-bearing bodies are the key factors affecting the cascading failure of heterogeneous hazard-bearing bodies. [ABSTRACT FROM AUTHOR]

Living systems are hierarchical control systems that display a small world network structure. In such structures, many smaller clusters are nested within fewer larger ones, producing a fractal-like structure with a 'power-law' cluster size distribution (a mereology). Just like their structure, the dynamics of living systems shows fractal-like qualities: the timeseries of inner message passing and overt behavior contain high frequencies or 'states' (treble) that are nested within lower frequencies or 'traits' (bass), producing a power-law frequency spectrum that is known as a 'state-trait continuum' in the behavioral sciences. Here, we argue that the power-law dynamics of living systems results from their power-law network structure: organisms 'vertically encode' the deep spatiotemporal structure of their (anticipated) environments, to the effect that many small clusters near the base of the hierarchy produce high frequency signal changes and fewer larger clusters at its top produce ultra-low frequencies. Such ultra-low frequencies exert a tonic regulatory pressure that produces morphological as well as behavioral traits (i.e., body plans and personalities). Nested-modular structure causes higher frequencies to be embedded within lower frequencies, producing a power-law state-trait continuum. At the heart of such dynamics lies the need for efficient energy dissipation through networks of coupled oscillators, which also governs the dynamics of non-living systems (e.q., earthquakes, stock market fluctuations). Since hierarchical structure produces hierarchical dynamics, the development and collapse of hierarchical structure (e.g., during maturation and disease) should leave specific traces in system dynamics (shifts in lower frequencies, i.e. morphological and behavioral traits) that may serve as early warning signs to system failure. The applications of this idea range from (bio)physics and phylogenesis to ontogenesis and clinical medicine. • Living systems universally display hierarchical dynamics (power-law frequency spectra). • We argue that this is due to the hierarchical structure of living systems. • Power-law frequency spectra define state-trait continua (e.g. body plans and personalities). • A collapse of hierarchical control may therefore cause (specific) changes in power-law frequency spectra. • This can serve as an early warning sign for system failure (e.g. physical and mental disorders). [ABSTRACT FROM AUTHOR]

• Propose a resilience assessment method for urban multi-modal transportation system. • The assessment index takes into account passenger demand and system supply. • Construct passenger flow transfer rules based on the passenger behaviour model. • Three transport modes (bus, subway and taxi) are integrated in the model. With the continuous construction of urban infrastructure, urban multi-modal transportation system (UMTS) has gradually become complex and intertwined, which makes the system more uncertain and vulnerable, especially under disruptions. Improving the resilience of UMTS is critical to maintaining urban reliability and sustainability. This paper aims to build effective models to assess the resilience of UMTS. To develop the resilience assessment model, we provide a comprehensive, dynamic index that considers passenger demand and infrastructure supply. Three transportation modes are considered: bus, subway and taxi, and a cascading failure model is simulated. Data from Singapore are collected to analyse resilience indicators' characteristics and explore relationship between resilience indicators and node measures. The results indicate that 1) when stations experience failure, it has the greatest impact on the accessibility of the transportation network, followed by efficiency and connectivity; 2) system resilience is negatively related to the node degree and node betweenness centrality of the attacked station; 3) beyond a certain threshold, continuing to increase stations' additional capacity does not significantly increase system resilience. The proposed resilience index can be used as an optimization goal during system design and recovery. The conclusions and recommendations can inform the management and improvement of urban transportation system resilience. [ABSTRACT FROM AUTHOR]

• The principle of post-earthquake traffic flow reassignment is proposed. • The post-earthquake SUE traffic reassignment based on cascading failure is obtained. • Effects of significant factors on the network efficiency and the number of link congestion are studied. • The top ten congestion-prone links under the cascading failure-based reliability assessment for post-earthquake performance of HBN are studied. This paper proposes a novel reliability assessment framework for post-seismic performance of highway bridge network that considers cascading failures caused by traffic flow redistribution. Firstly, the fragility curve of bridge is obtained by probabilistic seismic demand model. Then, we propose the impact factor of path choice probability to characterize the cascading failure of the network. The stochastic user equilibrium assignment of highway bridge network traffic flow is calculated based on the impact factor of path choice probability. To evaluate the network's efficiency and identify the congestion-prone links, the Monte Carlo simulation method is introduced to calculate the probability density curves of different influencing parameters. Finally, the framework proposed in this paper is utilized to analyze the congestion-prone links of the transportation network of some areas of Mianyang City and verify its applicability. [ABSTRACT FROM AUTHOR]

This paper proposes a novel cascading failure dynamics model for duplex weighted network with unequal flow distribution between layers and taking into account the collapse probability of overloaded nodes. Firstly, the parameter of failure elasticity is introduced to the redundancy capacity of the nodes to carry the load, and the expressions for the tolerance threshold of the entire network in different cases are derived. In addition, the cascading failure processes caused by different deliberate attack strategies are simulated on idealized networks and the IEEE39 network, respectively. Inflection points for the effectiveness of the two attack strategies are obtained, and tolerance thresholds of the theoretical calculations are compared and analyzed with the results of the numerical simulations. Meanwhile, our results indicate that the collapse probability and the redistribution rule are vital in the vulnerability of the network, and the protection mechanism is more effective against attacks on the node of lowest load. Finally, the duplex network becomes more robust as the parameter of failure elasticity increases. Furthermore, the tolerance threshold of the networks presents an ascending trend after dropping initially as the inter-layer distribution proportion increases, and the trend of the numerical simulation is consistent with the theoretical analysis. • A novel cascading failure model of two-layer weighted networks is presented. • We derive the expression of the tolerance threshold for overall duplex network. • Inflection points for the effectiveness of the two attack strategies are obtained. • Duplex networks become more robust as the parameter of failure elasticity increases. [ABSTRACT FROM AUTHOR]

Normal operation of metros and buses is essential for sustainable urban development. Studies have shown that a disaster occurring on one transport station leads to the cascading failure of transportation networks, but the functions will be restored successively after post-disaster repairs. However, most studies have focused on cascading failures, ignoring the impact of recovery propagation. Therefore, this study proposes a cascading failure and recovery model to illustrate the evolution process of a metro–bus double-layer network considering recovery propagation and investigates factors including failure and recovery spreading mechanisms, different initial loads, node capacities, and repair speeds. The proposed model is applied to an actual case study of Xi'an City under different scenarios. The effects of node capacity and repair speed exhibit a marginal decreasing trend. The coexistence of cascading failure and recovery propagation enhances network minimum performance. This study has implications for strategic development of sustainable and stable transportation systems. [ABSTRACT FROM AUTHOR]

• A high-speed train is modeled as an interdependent network. • A robustness metric is proposed based on network theory and practical factors. • Assessment and optimization models of resilience are constructed. • The tabu search algorithm is developed to solve the optimization problem. • The optimal repair strategy of failed units in the high-speed train is analyzed. High-speed trains (HSTs) are used to transport passengers to destinations efficiently and safely. However, when HST units fail, strategies for repairing them are not available. Hence, to optimize repair strategies, an interdependent network is used to model an HST, and a metric of resilience based on network theory is introduced. Based on practical factors, an interdependent machine–electricity–communication network (IMECN) and related cascading failure models are developed. Comprehensive robustness metrics for the IMECN and nodes are proposed considering the topology of networks and functional features of nodes. Accordingly, a resilience optimization model of the IMECN subject to disturbances is formulated and solved using a tabu search (TS) algorithm. Finally, a real-world HST is considered to analyze the optimal repair strategy for different numbers of failed nodes. Analysis results show that the recovery process under the optimal repair strategy has at most three stages. When a few nodes and less than half of the nodes fail, the highest and lowest resilience levels of the IMECN are achieved, respectively. Moreover, the characteristics of the preferentially repaired node in terms of importance, vulnerability, network type, and interdependency are analyzed. Results indicate that the optimal repair strategy is not necessarily determined by topological metrics. [ABSTRACT FROM AUTHOR]

• Four indexes are established which can reflect the characteristics comprehensive. • Cascading failure searching model is established based on non-cooperative game theory. • Immune quantum particle swarm optimization algorithm is used to solve the game model. To identify and assess the risk of cascading failure sequence in AC/DC hybrid power grid better, according to the grid topology structure and operation coupling characteristics, the four quantitative indexes of cascading failure sequence are established from the aspects of local link relationship with the topology structure, mutual influence between AC/DC systems, distribution characteristics of power flow operation and the support capacity of AC system to DC system. Considering the interaction of the established quantitative indexes, it is in line with the non-cooperative game problem. On this basis, a cascading failure sequence searching index game model is established to determine the weights of each quantitative index. For solving the optimal Nash equilibrium solutions and algorithm convergence of non-cooperative game model, the cooperative immune quantum particle swarm optimization algorithm is proposed. Considering the load loss of AC/DC hybrid power grid during the fault process, power flow off-limit severity index of risk assessment is carried out. Simulation results show that the established quantitative indexes and searching model of the cascading failure sequence in AC/DC hybrid power grid are more accurately. A realistic provincial AC/DC hybrid power grid in China is carried out to verify the practicability of the proposed method. [ABSTRACT FROM AUTHOR]

Cascading failures are widely found in hyper-networks. In this paper, a new cascading failure model based on couple map lattice is proposed in terms of the hyper-adjacent matrix and joint degree. The cascading failure model is rather universal describing the cascading failure behavior of k uniform hyper-network and many typical complex networks. Simulation results show that 3 uniform scale-free hyper-network is robust against random attacks but is vulnerable to deliberate attacks. In addition, a scale-free hyper-network is more robust than a general complex network against the same attack. Finally, an approximate solution to the disturbance threshold of k uniform scale-free hyper-network is obtained. [ABSTRACT FROM AUTHOR]

We analysis the cascading failure of interdependent weighted networks based on percolation theory and local weighted flow redistribution rule. The weight of a node is B i θ , where B i is the betweenness of the node. We assume that the two networks A and B of size N A and N B are BA networks, and suppose two different one-to-one interdependent network, one is random, the other based on nodes’ betweenness. Assume that a failed node in network A leads to a redistribution of the flow passing through it to its neighboring nodes and the interdependent node in network B also to be disabled, where the two failure factors happen concurrently, or successively. We find that the one-to-one random interdependent weighted complex network reaches the strongest robustness level when the weight parameter θ =0.5, no matter cascading failure caused by two failure factors happen concurrently, or successively. And when the interdependent relationship based on nodes’ betweenness, θ =0.7 to get the strongest robustness level. [ABSTRACT FROM AUTHOR]

For R&D projects, the cascading failure among R&D firms will lead to the schedule risks of the R&D tasks, which may lead to potential severe consequences. It is necessary to develop mitigation strategies against cascading failures, so as to reduce schedule risks of R&D projects. Firstly, we propose the BBV algorithm to build the R&D network. Secondly, we build the model of the cascading failures of the R&D network based on the CA model. Thirdly, we develop the mitigation strategies against the schedule risks of the R&D project through controlling the cascading failure. Finally, we analyze different effectiveness of these mitigation strategies against the cascading failures of the R&D network under different values of some critical parameters and different attack strategies. The simulation results show that with the increase of μ and β , the schedule risk of the task network gradually decreases. With the increase of the control parameters ζ , the schedule risk of the task network gradually increases. In any case, the effectiveness of global immunization is better than local immunization, when we know the global information, HI is better than KI, and when we only know the local information, IAI is better than AI. The effectiveness of mitigation strategy under random attack strategy is the best, followed by high-degree attack strategy and high-centrality attack strategy. This provides a new useful theoretical basis on how to keep the safety of the schedule of the R&D project proactively against the cascading failure of the R&D firms in the real world. [ABSTRACT FROM AUTHOR]

The robustness of realistic infrastructure systems is a significant and long-term research question, which has gotten some constructive outcomes borrowing the framework of complex networks. In this paper, we further explore the method about utilizing optimization algorithms to enhance robustness of interdependent networks. Firstly, we propose a novel particle swarm optimization algorithm with an information feedback mechanism to achieve better performance on complex problems. Secondly, we analyze the solutions from initial loads and types of failed nodes resulted by our algorithm. Interestingly, relative to traditional setup, our algorithm indeed produces a robust resource allocation pattern for interdependent networks, where middle-degree nodes are assigned more tolerance. [ABSTRACT FROM AUTHOR]

Margin trading in which investors purchase shares with money borrowed from brokers is blamed to be a major cause of the 2015 Chinese stock market crash. We propose a cascading failure model and examine how an increase in margin trading increases share price vulnerability. The model is based on a bipartite graph of investors and shares that includes four margin trading factors, (i) initial margin k , (ii) minimum maintenance r , (iii) volatility v , and (iv) diversity s . We use our model to simulate margin trading and observe how the share prices are affected by these four factors. The experimental results indicate that a stock market can be either vulnerable or stable. A stock market is vulnerable when an external shock can cause a cascading failure of its share prices. It is stable when its share prices are resilient to external shocks. Furthermore, we investigate how the cascading failure of share price is affected by these four factors, and find that by increasing v and r or decreasing k we increase the probability that the stock market will experience a phase transition from stable to vulnerable. It is also found that increasing s decreases resilience and increases systematic risk. These findings could be useful to regulators supervising margin trading activities. [ABSTRACT FROM AUTHOR]

Recently, the robustness of networks under cascading failure has attracted extensive attention. Different from previous studies, we concentrate on how to improve the robustness of the networks from the perspective of intelligent optimization. We establish two multi-objective optimization models that comprehensively consider the operational cost of the edges in the networks and the robustness of the networks. The NNIA (Non-dominated Neighbor Immune Algorithm) is applied to solve the optimization models. We finished simulations of the Barabási–Albert (BA) network and Erdös–Rényi (ER) network. In the solutions, we find the edges that can facilitate the propagation of cascading failure and the edges that can suppress the propagation of cascading failure. From the conclusions, we take optimal protection measures to weaken the damage caused by cascading failures. We also consider actual situations of operational cost feasibility of the edges. People can make a more practical choice based on the operational cost. Our work will be helpful in the design of highly robust networks or improvement of the robustness of networks in the future. [ABSTRACT FROM AUTHOR]

Cascading failure has already become one of the vital issues in network science. By considering realistic network operational settings, we propose the congestion function to represent the congested extent of node and construct a local congestion-aware routing strategy with a tunable parameter. We investigate the cascading failures on the Internet triggered by deliberate attacks. Simulation results show that the tunable parameter has an optimal value that makes the network achieve a maximum level of robustness. The robustness of the network has a positive correlation with tolerance parameter, but it has a negative correlation with the packets generation rate. In addition, there exists a threshold of the attacking proportion of nodes that makes the network achieve the lowest robustness. Moreover, by introducing the concept of time delay for information transmission on the Internet, we found that an increase of the time delay will decrease the robustness of the network rapidly. The findings of the paper will be useful for enhancing the robustness of the Internet in the future. [ABSTRACT FROM AUTHOR]

Growing scientific evidence suggests that risks due to failure of critical infrastructures (CIs) will increase worldwide, as the frequency and intensity of extreme weather events (EWEs) induced by climate change increases. Such risks are difficult to estimate due to the increasing complexity and interconnectedness of CIs and because information sharing regarding the vulnerabilities of the different CIs is limited. This paper proposes a methodology for risk analysis of systems of interdependent CIs to EWEs. The methodology is developed and carried out for the Port of Rotterdam area in the Netherlands, which is used as a case study. The case study includes multiple CIs that belong to different sectors and can be affected at the same time by an initiating EWE. The proposed methodology supports the assessment of common cause failures that cascade across CIs and sectors. It is based on a simple, user-friendly approach that can be used by CIs owners and operators. The implementation of the methodology has shown that the severity of cascading effects is strongly influenced by the recovery time of the different CIs due to the initiating EWE and that cascading effects that result from a disruption in a single CI develop differently from cascading effects that result from common cause failures. For most CIs, vulnerabilities from EWEs on the CI level will be higher than the cascading risks of common cause failures on the system of CIs; moreover, cascading risks for a CI will increase after its recovery from the event. [ABSTRACT FROM AUTHOR]