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This paper combines the digital twin system modeling method to conduct an in-depth study and analysis of graph-theoretic combinatorial optimization. This paper provides new ideas and approaches for optimal numerical analysis work by studying the digital twin modeling method that integrates digital modeling and graph theory combination, provides theoretical support for safe, stable, and economic operation of the system, proposes a solution for digital twin model based on big data platform, focuses on the nearest neighbor propagation (AP) and graph theory combination, solves the digital twin real-time monitoring data asynchronous, incomplete problem, and applies the algorithm to the digital twin model based on the big data platform for data preprocessing to achieve better results. This paper also presents a web-based digital twin system based on intelligent practical needs, analysis, and comparison of existing models, combined with digital twin technology, detailing the differences and connections between the various levels of numerical analysis and the implementation of this data in various fields, such as user management, equipment health management, product quality management, and workshop 3D navigation and detailed modeling of the digital twin system based on this numerical analysis to realize remote online monitoring, analysis, and management. In this paper, for the numerical analysis process, firstly, the key technologies of modeling and simulation operation control of production line based on digital twin are studied, and the rapid response manufacturing system based on a digital twin is designed and validated. Secondly, a scheduling technology framework for capacity simulation evaluation and optimization is established, and batching optimization, outsourcing decision, and rolling scheduling techniques are thus proposed to form a batching optimization algorithm based on priority rules, which realizes batching processing, outsourcing decision, and rolling scheduling of production orders to optimize equipment utilization and capacity. Finally, digital twin-based modeling is designed, and the validation results demonstrate the system's superior performance in achieving information interaction between physical and virtual production lines, optimization of numerical analysis, and display of results. [ABSTRACT FROM AUTHOR]

This paper studies the complexity analysis in production between competition and R&D for a traditional energy vehicles enterprise and a new energy vehicles enterprise under the introduction of corporate average fuel consumption credits and new energy vehicle credits mandate. From the internal perspective of market complexity evolution, this paper analyzes the internal mechanism of market competition fluctuation and discusses the influence of different corresponding speeds of enterprises on market stability through the nonlinear dynamics' theory. The research results show that the adjustment coefficient of R&D investment and the price coefficient of credit transactions are the key factors affecting the competitive strategies of the two companies. The difference between these two factors will even change the relative R&D investment intensity, relative profitability, and market stability of the two companies in a balanced state. In addition, the numerical analysis showed that the time-delay feedback control method could control the unstable behavior of the dynamic system efficiently and quickly and make the market quickly recover a stable and orderly state, which provided a scientific basis for decision makers to effectively solve the market instability. [ABSTRACT FROM AUTHOR]

In this paper, we use digital twin technology to conduct in-depth analysis and research on the modeling of complex systems for smart aging. The solution of the digital twin model based on a big data platform is proposed, and the problem of asynchronous and incomplete digital twin real-time monitoring data is solved, and the algorithm is applied to the digital twin model based on the big data platform for data preprocessing to achieve better results. To improve the real-time data transmission, the OPCUA information modeling method is optimized by using node merging and adaptive compression, which statutes the system data and achieves the effect of information fusion. The Web protocol is also used to unify the digital twin information interaction form. After experimental testing, the effectiveness of the information modeling scheme designed in this paper is verified. The fall detection results based on the digital twin selected thresholds are significantly better than the experimental results of the manually set threshold method; the thresholds set by the digital twin can more accurately identify daily behaviors, especially the more violent daily behaviors such as lying down, and the accurate alarm rate of the falling behavior reaches 92.5%. In contrast, the artificially set thresholds have a lower overall recognition rate for human behaviors and are prone to misclassification, with a misclassification rate of 3.8%. Therefore, it can be determined that using the digital twin method to set feature thresholds is better than the manual setting threshold method in terms of detection accuracy, and the digital twin method is chosen to select the thresholds for each stage of the fall process in this project. The validation results demonstrate the system's excellence in information interaction, optimization of numerical analysis, and display of results for smart aging. [ABSTRACT FROM AUTHOR]

This paper is devoted to the analysis and design of H∞ filtering for discrete-time Takagi–Sugeno (TS) fuzzy systems with time-varying delays. By using the delay-partitioning method, more systematic information is introduced, which can reduce the conservatism of the conclusion. By constructing an appropriate Lyapunov functional and combining with a newly Wirtinger-based summation inequality, the existence condition of the H∞ filter is obtained. Thus, utilizing the contract matrix transformation method, the H∞ filter design for discrete-time TS fuzzy systems with time-varying delay based on LMI is proposed. Finally, a few numerical analysis results are given to prove the effectiveness of the method. [ABSTRACT FROM AUTHOR]

Mass customization logistics service mode provides a new way to maintain the sustainable cooperative relationship between customers and integrators. One of the key factors to maintain the sustainable development of logistics service supply chain under MC mode is to locate a suitable customer order decoupling point (CODP) location. This paper investigates the problem of CODP in the logistics service supply chain based on the fuzzy set theory under the mass customization mode. With the help of a fuzzy QFD method and a new service quality function that we constructed, this paper quantifies the quality of a logistics service when the LSI selects a different CODP. Then, the fuzzy set of the high-quality logistics service and the fuzzy set of the satisfactory delivery time are built. Based on those two new fuzzy sets, this paper builds a new fuzzy programming model on CODP positioning. The solving methods of this model under different conditions are given. Finally, the influence of some important parameters on the optimal CODP position is studied by sensitivity analysis on a specific numerical case. [ABSTRACT FROM AUTHOR]

This paper first proposes a European option pricing method for deposit insurance based on triangular intuitionistic fuzzy numbers. In the proposed method, we take into account the randomness and fuzziness of bank asset value simultaneously, and hence, the method can adequately reflect the high uncertainty of bank asset value. This method fuzzifies the value of bank asset, resubmits it into the original deposit insurance option pricing model as a fuzzy random variable, and then gives an analytic formula of deposit insurance rates using a risk-neutral method. After this, we have also conducted a numerical analysis. In specific, we have obtained the premium interval and presented the static analysis of key parameters. Finally, seven small- and middle-sized banks in Hunan Province in China are used as examples to validate the proposed interval pricing model. The Black-Scholes option pricing model and Yoshida's triangular fuzzy model are also employed for comparison. The research results show that the interval rates obtained from the proposed European option pricing method for deposit insurance can better reflect the uncertainty of bank asset evaluation than the fixed rates obtained from the Black-Scholes option pricing model. Moreover, the model proposed in this paper is also superior to Yoshida's model in practice. [ABSTRACT FROM AUTHOR]

In this paper, we study the basket CDS pricing with two defaultable counterparties based on the reduced-form model. The default jump intensities of the reference firms and counterparties are all assumed to follow the mean-reverting constant elasticity of variance (CEV) processes. Taking the Vasicek process which is a special case of CEV process as an example, the approximate analytic solutions of the joint survival probability density, the probability densities of the first default and the first two defaults can be solved by using PDE method. In addition, we also extend the Vasciek process to the Vasciek process with cojumps and obtain the approximate closed-form solutions of the relevant default probability densities. Then with the expressions of the probability densities, we can get the formula of the basket CDS price with two defaultable counterparties. In the numerical analysis, we do sensitivity analysis and compare the basket CDS prices under our model with that with only one defaultable counterparty. The numerical results show that our model can be applied into practice. [ABSTRACT FROM AUTHOR]

Logistics distribution plays an important role in the operation of e-commerce firms. This paper considers two logistics distribution modes with service competition: the e-commerce platform self-distribution (SDL) mode and third-party logistics (TPL) mode. By introducing consumer behavior into the model, we examine the competition between two firms with the same functionalities in the context of e-commerce. According to the real scene, we build the corresponding mathematical optimization model. Each firm needs to decide a logistics distribution mode and a corresponding price for the selected logistics mode. We first analyze the two firms chosen logistics modes and prices simultaneously and then extend it to Stackelberg game situation. We find out the optimal strategy for two firms. Finally, we propose numerical analysis to identify our models and provide a series of managerial insights. [ABSTRACT FROM AUTHOR]

In this paper, complex dynamical behaviors of a predator-prey system with the Beddington–DeAngelis functional response and the Allee-like effect on predator were studied by qualitative analysis and numerical simulations. Theoretical derivations have given some sufficient and threshold conditions to guarantee the occurrence of transcritical, saddle-node, pitchfork, and nondegenerate Hopf bifurcations. Computer simulations have verified the feasibility and effectiveness of the theoretical results. In short, we hope that these works could provide a theoretical basis for future research of complexity in more predator-prey ecosystems. [ABSTRACT FROM AUTHOR]

This paper investigates the pricing of discretely sampled variance swaps under a Markov regime-switching jump-diffusion model. The jump diffusion, as well as other parameters of the underlying stock's dynamics, is modulated by a Markov chain representing different states of the market. A semi-closed-form pricing formula is derived by applying the generalized Fourier transform method. The counterpart pricing formula for a variance swap with continuous sampling times is also derived and compared with the discrete price to show the improvement of accuracy in our solution. Moreover, a semi-Monte-Carlo simulation is also presented in comparison with the two semi-closed-form pricing formulas. Finally, the effect of incorporating jump and regime switching on the strike price is investigated via numerical analysis. [ABSTRACT FROM AUTHOR]

With the rapid development of e-commerce, online retailing has become an important part of the market. In order to improve market competitiveness and increase market share, more and more retailers have opened both regular offline channel and online e-tail channel to sell products. Then how to price becomes an urgent problem for upstream manufacturers and dual-channel retailers when there is price competition between regular channel and e-tail channel, especially when consumers have peer-induced fairness concerns. However, linking consumers' behavioral factors such as fairness concerns to pricing decisions of mixed retail and e-tail channels draws little attention in the literature on supply chain management. This paper incorporates "consumers' peer-induced fairness concerns" (CPFC) into pricing decisions in a dyadic supply chain, where dual-channel retailer obtains products from manufacturers and then sells products to consumers through both regular channel and e-tail channel. We use game-theoretic models to analyze the equilibrium pricing strategies under the setting with "symmetry consumers' peer-induced fairness concerns" (SCPFC) and with "asymmetry consumers' peer-induced fairness concerns" (ACPFC), respectively. Detailed comparisons and numerical analysis are further conducted to examine the impacts of different types of CPFC on equilibrium pricing strategies and profits. [ABSTRACT FROM AUTHOR]

With the rapid development of e-commerce, online retailing has become an important part of the market. In order to improve market competitiveness and increase market share, more and more retailers have opened both regular offline channel and online e-tail channel to sell products. Then how to price becomes an urgent problem for upstream manufacturers and dual-channel retailers when there is price competition between regular channel and e-tail channel, especially when consumers have peer-induced fairness concerns. However, linking consumers' behavioral factors such as fairness concerns to pricing decisions of mixed retail and e-tail channels draws little attention in the literature on supply chain management. This paper incorporates "consumers' peer-induced fairness concerns" (CPFC) into pricing decisions in a dyadic supply chain, where dual-channel retailer obtains products from manufacturers and then sells products to consumers through both regular channel and e-tail channel. We use game-theoretic models to analyze the equilibrium pricing strategies under the setting with "symmetry consumers' peer-induced fairness concerns" (SCPFC) and with "asymmetry consumers' peer-induced fairness concerns" (ACPFC), respectively. Detailed comparisons and numerical analysis are further conducted to examine the impacts of different types of CPFC on equilibrium pricing strategies and profits. [ABSTRACT FROM AUTHOR]

Price competition has become a universal commercial phenomenon nowadays. This paper considers a dynamic Bertrand price game model, in which enterprises have heterogeneous expectations. By the stability theory of the dynamic behavior of the Bertrand price game model, the instability of the boundary equilibrium point and the stability condition of the internal equilibrium point are obtained. Furthermore, bifurcation diagram, basin of attraction, and critical curve are introduced to investigate the dynamic behavior of this game. Numerical analysis shows that the change of model parameters in a dynamic system has a significant impact on the stability of the system and can even lead to complex dynamic behaviors in the evolution of the entire economic system. This kind of complex dynamic behavior will cause certain damage to the stability of the whole economic system, causing the market to fall into a chaotic state, which is manifested as a kind of market disorder competition, which is very unfavorable to the stability of the economic system. Therefore, the chaotic behavior of the dynamical system is controlled by time-delay feedback control and the numerical analysis shows that the effective control of the dynamical system can be unstable behavior and the rapid recovery of the market can be stable and orderly. [ABSTRACT FROM AUTHOR]

In complex networks, mining important nodes has been a matter of concern by scholars. In recent years, scholars have focused on mining important nodes in undirected unweighted complex networks. But most of the methods are not applicable to directed weighted complex networks. Therefore, this paper proposes a Two-Way-PageRank method based on PageRank for further discussion of mining important nodes in directed weighted complex networks. We have mainly considered the frequency of contact between nodes and the length of time of contact between nodes. We have considered the source of the nodes (in-degree) and the whereabouts of the nodes (out-degree) simultaneously. We have given node important performance indicators. Through numerical examples, we analyze the impact of variation of some parameters on node important performance indicators. Finally, the paper has verified the accuracy and validity of the method through empirical network data. [ABSTRACT FROM AUTHOR]

The objective of this paper is to discuss finite-time bounded synchronization for a class of the growing complex network with nondelayed and delayed coupling. In order to realize finite-time synchronization of complex networks, a new finite-time stable theory is proposed; effective criteria are developed to realize synchronization of the growing complex dynamical network in finite time. Moreover, the error of two growing networks is bounded simultaneously in the process of finite-time synchronization. Finally, some numerical examples are provided to verify the theoretical results established in this paper. [ABSTRACT FROM AUTHOR]

This paper investigates the feedback control for networked discrete-time finite-distributed delays with quantization and packet dropout, and systems induce the H∞ control problem. The compensation scheme occurs in a random way. The quantization of system state or output signal is in front of being communicated. It is shown that the design of both a state feedback controller and an observer-based output feedback controller can be achieved, which ensure the asymptotical stability as well as a prescribed H∞ performance of the resulting closed-loop system satisfying dependence on the size of the discrete and distributed delays. Numerical examples are given to illustrate the effectiveness and applicability of the design method in this paper. [ABSTRACT FROM AUTHOR]

This paper proposes a second-order jump diffusion model to study the jump dynamics of stock market returns via adding a jump term to traditional diffusion model. We develop an appropriate maximum likelihood approach to estimate model parameters. A simulation study is conducted to evaluate the performance of the estimation method in finite samples. Furthermore, we consider a likelihood ratio test to identify the statistically significant presence of jump factor. The empirical analysis of stock market data from North America, Asia, and Europe is provided for illustration. [ABSTRACT FROM AUTHOR]

This paper proposes and investigates a special class of explicit Runge-Kutta-Nyström (RKN) methods for problems in the form y′′(x)=f(x,y,y′) including third derivatives and denoted as STDRKN. The methods involve one evaluation of second derivative and many evaluations of third derivative per step. In this study, methods with two and three stages of orders four and five, respectively, are presented. The stability property of the methods is discussed. Numerical experiments have clearly shown the accuracy and the efficiency of the new methods. [ABSTRACT FROM AUTHOR]

Fractional order delay differential-algebraic equations have the characteristics of time lag and memory and constraint limit. These yield some difficulties in the theoretical analysis and numerical computation. In this paper, we are devoted to solving them by the waveform relaxation method. The corresponding convergence results are obtained, and some numerical examples show the efficiency of the method. [ABSTRACT FROM AUTHOR]

This paper mainly addresses the issue of how to effectively inhibit viral spread by means of dynamic countermeasure. To this end, a controlled node-level model with nonlinear infection and countermeasure rates is established. On this basis, an optimal control problem capturing the dynamic countermeasure is proposed and analyzed. Specifically, the existence of an optimal dynamic countermeasure scheme and the corresponding optimality system are shown theoretically. Finally, some numerical examples are given to illustrate the main results, from which it is found that (1) the proposed optimal strategy can achieve a low level of infections at a low cost and (2) adjusting nonlinear infection and countermeasure rates and tradeoff factor can be conductive to the containment of virus propagation with less cost. [ABSTRACT FROM AUTHOR]

The paper incorporates cooperative game theory into a real option method in a foreign direct investment setting and examines the operational decisions of a multinational corporation in a cooperative framework, where the corporation is endowed with an abandonment option and shares its profit with the host country. In particular, we investigate how the abandonment options affect the optimal investment timing and the optimal profit share of a foreign direct investment using a real option game method. We show that the flexibility of the abandonment option induces the corporation to investment earlier, which indicates the negative effects on investment trigger. The result is consistent with intuition since the abandonment option provides insurance and thus reduces the overall risk of the project. We also find that the introduction of the abandonment option reduces the optimal profit share in a cooperative framework and in turn the lower profit share increases the investment trigger, thereby having a positive effect on the investment threshold to hinder the investment. By numerical analysis, we find that the overall effect of the abandonment options is inversely related to the investment trigger. These findings provide quantitative analysis about the decisions regarding cooperation in international investment extraction projects. [ABSTRACT FROM AUTHOR]

This paper develops a type of data-driven networked optimal iterative learning control strategy for a class of discrete linear time-varying systems with one-operation Bernoulli-type communication delays. In terms of the stochastic Bernoulli-type one-operation communication delayed inputs and outputs, the previous-iteration synchronous compensations are adopted. By means of deriving gradients of two types of objective functions that express the optimal approximation of the system matrix and the minimal tracking error, the strategy approximates the system matrix and upgrades the control inputs in an interact mode as the iteration evolves. By taking advantage of matrix theory and statistical technique, it is derived that the approximation discrepancy of the system matrix is bounded and the mathematical expectation of the tracking error vanishes as the iteration goes on. Numerical simulations manifest the validity and effectiveness. [ABSTRACT FROM AUTHOR]

In this paper, the global O(t-α) synchronization problem is investigated for a class of fractional-order neural networks with time delays. Taking into account both better control performance and energy saving, we make the first attempt to introduce centralized data-sampling approach to characterize the O(t-α) synchronization design strategy. A sufficient criterion is given under which the drive-response-based coupled neural networks can achieve global O(t-α) synchronization. It is worth noting that, by using centralized data-sampling principle, fractional-order Lyapunov-like technique, and fractional-order Leibniz rule, the designed controller performs very well. Two numerical examples are presented to illustrate the efficiency of the proposed centralized data-sampling scheme. [ABSTRACT FROM AUTHOR]

In this paper, a robust, effective, and accurate numerical approach is proposed to obtain the numerical solution of fractional differential equations. The principal characteristic of the approach is the new orthogonal functions based on shifted Legendre polynomials to the fractional calculus. Also the fractional differential operational matrix is driven. Then the matrix with the Tau method is utilized to transform this problem into a system of linear algebraic equations. By solving the linear algebraic equations, the numerical solution is obtained. The approach is tested via some examples. It is shown that the FLF yields better results. Finally, error analysis shows that the algorithm is convergent. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new hybrid direct search method where a frame-based PRP conjugate gradients direct search algorithm is combined with radial basis function interpolation model. In addition, the rotational minimal positive basis is used to reduce the computation work at each iteration. Numerical results for solving the CUTEr test problems show that the proposed method is promising. [ABSTRACT FROM AUTHOR]

This paper is devoted to stochastic delayed one-predator and two-competing-prey systems with two kinds of different functional responses. By establishing appropriate Lyapunov functions, the globally positive solution and stochastic boundedness are investigated. In some case, the stochastic permanence and extinction are also obtained. Moreover, sufficient conditions of the global asymptotic stability of the system are established. Finally, some numerical examples are provided to explain our conclusions. [ABSTRACT FROM AUTHOR]

This paper considers the control problem of dynamically complex networks with saturation couplings. Two novel control schemes in terms of adaptive control are presented to deal with such saturation couplings. Based on the robust idea, the underlying complex network is firstly transformed into a strongly connected network having time-varying uncertainty. However, the upper bound of uncertainty is unknown. Because of such an unavailable bound, a kind of adaptive controller added to each node is proposed such that the closed-loop auxiliary network is uniformly bounded. In particular, the original system states are asymptotically stable. Moreover, in order to avoid adding the desired controller to every node, another different kind of adaptive controller based on the pinning control idea is proposed. Compared with the former method, it is only applied to a part of nodes and has a good operability. Finally, a numerical example is provided to show the effectiveness of our results. [ABSTRACT FROM AUTHOR]

Rail and transit-oriented-development (TOD) projects are simultaneously optimized in this paper, with special consideration given to yearly variation and spatial and temporal correlation of population densities. In the proposed model, the objective is to minimize the investment risk of integrated rail and TOD projects with a given required expected return on investment. The investment risk is optimized based on closed-form solutions of the design variables, including rail line length, the number of TOD projects, and the number of housing units in each TOD project. The closed-form solutions are given explicitly under the assumption of social welfare maximization. It is found that underestimation exists for rail and TOD projects without consideration of the correlation of spatial and temporal population densities. TOD projects can greatly improve the return on investment of the rail operator. A numerical example is also presented. [ABSTRACT FROM AUTHOR]

This paper investigates the channel coordination of a supply chain (SC) consisting of a loss-averse retailer and a risk-neutral supplier under yield and demand uncertainties. Three existing contracts are analyzed. Our results demonstrate that the buyback (BB) and quantity flexibility (QF) contracts can not only coordinate the supply chain but also lead to Pareto improvement for each player, while the wholesale price (WP) contract fails to coordinate the chain due to the effects of double marginalization and risk preference. For comparison, a chain with a risk-neutral retailer is also analyzed. Furthermore, numerical examples are provided to demonstrate the effectiveness of the coordination contracts, and the impacts of loss aversion and random yield on the decision-making behaviors and system performance are then discussed. [ABSTRACT FROM AUTHOR]

Market crashes often appear in daily trading activities and such instantaneous occurring events would affect the stock prices greatly. In an unstable market, the volatility of financial assets changes sharply, which leads to the fact that classical option pricing models with constant volatility coefficient, even stochastic volatility term, are not accurate. To overcome this problem, in this paper we put forward a dynamic elasticity of variance (DEV) model by extending the classical constant elasticity of variance (CEV) model. Further, the partial differential equation (PDE) for the prices of European call option is derived by using risk neutral pricing principle and the numerical solution of the PDE is calculated by the Crank-Nicolson scheme. In addition, Kalman filtering method is employed to estimate the volatility term of our model. Our main finding is that the prices of European call option under our model are more accurate than those calculated by Black-Scholes model and CEV model in financial crashes. [ABSTRACT FROM AUTHOR]

This paper is concerned with the numerical stability of a class of nonlinear neutral delay differential equations. The numerical stability results are obtained for (k,l)-algebraically stable Runge-Kutta methods when they are applied to this type of problem. Numerical examples are given to confirm our theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the problem of H∞ fault detection for a class of linear discrete time-varying descriptor systems with missing measurements, and the missing measurements are described by a Bernoulli random binary switching sequence. We first translate the H∞ fault detection problem into an indefinite quadratic form problem. Then, a sufficient and necessary condition on the existence of the minimum is derived. Finally, an observer-based H∞ fault detection filter is obtained such that the minimum is positive and its parameter matrices are calculated recursively by solving a matrix differential equation. A numerical example is given to demonstrate the efficiency of the proposed method. [ABSTRACT FROM AUTHOR]

To design an efficient and economical timetable for a heavily congested urban rail corridor, a scheduling model is proposed in this paper. The objective of the proposed model is to find the departure time of trains at the start terminal to minimize the system cost, which includes passenger waiting cost and operating cost. To evaluate the performance of the timetable, a simulation model is developed to simulate the detailed movements of passengers and trains with strict constraints of station and train capacities. It assumes that passengers who arrive early will have more chances to access a station and board a train. The accessing and boarding processes of passengers are all based on a first-come-first-serve basis. When a station is full, passengers unable to access must wait outside until the number of waiting passengers at platform falls below a given value. When a train is full, passengers unable to board must wait at the platform for the next train to arrive. Then, based on the simulation results, a two-stage genetic algorithm is introduced to find the best timetable. Finally, a numerical example is given to demonstrate the effectiveness of the proposed model and solution method. [ABSTRACT FROM AUTHOR]

This paper presents a third order of accuracy stable difference scheme for the approximate solution of multipoint nonlocal boundary value problem of the hyperbolic type in a Hilbert space with self-adjoint positive definite operator. Stability estimates for solution of the difference scheme are obtained. Some results of numerical experiments that support theoretical statements are presented. [ABSTRACT FROM AUTHOR]

Conventional DEA models make no hypothesis concerning the internal operations in a static situation. To open the “black box” and work with dynamic assessment issues synchronously, we put forward a hybrid model for evaluating the relative efficiencies of a set of DMUs over an observed time period with a composite of network DEA and dynamic DEA. We vertically deal with intermediate products between divisions with assignable inputs in the network structure and, horizontally, we extend network structure by means of a dynamic pattern with unrelated activities between two succeeding periods. The hybrid dynamic network DEA model proposed in this paper enables us to (i) pry into the internal operations of DEA by another network structure, (ii) obtain dynamic change of period efficiency, and (iii) gain the overall dynamic efficiency of DMUs over the entire observed periods. We finally illustrate the calculation procedure of the proposed approach by a numerical example. [ABSTRACT FROM AUTHOR]

An Euler difference scheme for a three-dimensional predator-prey model is considered and we introduce a new approach to show the global stability of the scheme. For this purpose, we partition the three-dimensional space and calculate the sign of the rate change of population of species in each partitioned region. Our method is independent of dimension and then can be applicable to other dimensional discrete models. Numerical examples are presented to verify the results in this paper. [ABSTRACT FROM AUTHOR]

We make further attempts to investigate equilibrium stability of a nonlinear Cournot duopoly game. Our studies in this paper focus on the cooperation that may be obtained among duopolistic firms. Discrete time scales under the assumption of unknown inverse demand function and linear cost are used to build our models in the proposed games. We introduce and study here an adjustment dynamic strategy beside the so-called tit-for-tat strategy. For each model, the stability analysis of the fixed point is analyzed. Numerical simulations are carried out to show the complex behavior of the proposed models and to point out the impact of the models’ parameters on the cooperation. [ABSTRACT FROM AUTHOR]

Based on a special matrix structure, the projective synchronization control laws of the hyperchaotic financial systems are proposed in this paper. Put a hyperchaotic financial system as the drive system, via transformation of the system state variables, construct its response system, and then design the controller based on the special matrix structure. The given scheme is applied to achieve projective synchronization of the different hyperchaotic financial systems. Numerical experiments demonstrate the effectiveness of the method. [ABSTRACT FROM AUTHOR]

This paper proposes a rumor spreading model which examines how the memory effects rate changes over time in artificial network and a real social network. This model emphasizes a special rumor spreading characteristic called “the cumulative effects of memory.” A function p(t) reflecting the cumulative memory effects is established, which replaces the constant rate of memory effects in the traditional model. Further, rumor spreading model simulations are conducted with different parameters in three artificial networks. The results show that all the parameters but the initial memory rate of memory effects function have a significant impact on rumor spreading. At the same time, the simulation results show that the final size of the stiflers is sensitive to the average degree k when it is small but is not sensitive to k when the average degree is greater than a certain degree. Finally, through investigations on the Sina Microblog network, the numerical solutions show that the peak value and final size of the rumor spreading are much larger under a variable memory effects rate than under a constant rate. [ABSTRACT FROM AUTHOR]