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• The paper is the first batch that tries to inquiry the GPS of the PDIMNNs. Furthermore, unlike the previous literature [11,21,35] , the nonlinear substitution that converts the PDs system to a constant delays system is not used. Because the subsequent pro-cessing of the converted system is complicated, this paper directly performs on the original PDs system. • The paper employs the non-reduced-order method, which r-efrains the double-dimensional problem after reduced-order [3–5,23,24]. In practical applications, the method is more ponderable and si-gnificative for second-order scheme under controller. • In the paper, devise both the feedback controller and the adaptive controller for the first time to achieve the GPS of the PD-IMNNs. The advantages of the two types of controllers are compar-ed through numerical examples and simulations. The mathematical model is closer to reality, and selecting the appropriate controller in application can further reduce control expenses. This article probes into the global polynomial stabilization (GPS) of proportional delayed inertial memristive neural networks (PDIMNNs). Here, ruling out the reduced-order way, discuss the GPS of PDIMNNs under the second-order scheme directly. Firstly, a feedback controller is designed to make the system self-stabilizing. By designing suitable Lyapunov functional with adjustable parameters and combining with inequality techniques, two algebraic criteria are obtained to realize the GPS of the PDIMNNs. Owing to the conservatism caused by the ineluctable inequality scaling, it is worth noting that the controller gains are greater than the actual requirements. To further save control expenses, employing an adaptive controller to make the system stabilized. Finally, three numerical examples which sustain the usability of the obtained theoretical conclusions are shown. [ABSTRACT FROM AUTHOR]

In order to better describe the mechanism of rumor propagation, suppress rumor propagation. This paper examines the influence of true information disseminators on individuals and rumor spreaders who are affected by the public opinion environment. It is found by comparing those who have true information and those who do not have true information in the population. When there are true information disseminators in the crowd, it can effectively control the turn of individuals affected by the public opinion environment to the spread of rumors, and increase the turn of individuals affected by the public opinion environment to the true information disseminators. In addition, this paper analyzes the problems related to the optimal control of the rumor propagation model, and proposes some policies to increase the number of true information disseminators and reduce the number of rumor propagators, so as to better control the spread of rumors. Finally, numerical simulations verify the inhibitory effect of true information disseminators on the spread of rumors. It can be seen from the figure that the earlier the true information disseminator appears, the greater the number of true information disseminators, and the more obvious the inhibitory effect on the spread of rumors. • Add true information spreaders to the crowd, compared and discussed the differences with and without it. • Increasing the number of true information spreaders, can reduce the influence of public opinion and weaken rumor spreading. • It is concluded that the optimal control is helpful to reduce the number of rumors spreading in the crowd. [ABSTRACT FROM AUTHOR]

The property of reversibility is quite meaningful for the classic theoreticabl computer science model, cellular automata. This paper focuses on the reversibility of general one-dimensional (1D) linear cellular automata (LCA), under null boundary conditions over the finite field Z p . Although the existing approaches have split the reversibility challenge into two sub-problems: calculate the period of reversibility first, then verify the reversibility in a period, they are still exponential in the size of the CA's neighborhood. In this paper, we use two efficient algorithms with polynomial complexity to tackle these two challenges, making it possible to solve large-scale reversible LCA, which substantially enlarge its applicability. Finally, we provide an interesting perspective to inversely generate a 1D LCA from a given period of reversibility. [ABSTRACT FROM AUTHOR]

• P-Lingua is a well-known programming language for membrane systems. • P-Lingua 5 features customized P system variants definitions, including semantics. • Derivation modes and simulation directives are now described in P-Lingua 5 code. • P-Lingua 5 software toolkit (compiler and simulator) is backward-compatible. Membrane computing is a massively parallel and non-deterministic bioinspired computing paradigm whose models are called P systems. Validating and testing such models is a challenge which is being overcome by developing simulators. Regardless of their heterogeneity, such simulators require to read and interpret the models to be simulated. To this end, P-Lingua is a high-level P system definition language which has been widely used in the last decade. The P-Lingua ecosystem includes not only the language, but also libraries and software tools for parsing and simulating membrane computing models. Each version of P-Lingua supported new types or variants of P systems. This leads to a shortcoming: Only a predefined list of variants can be used, thus making it difficult for researchers to study custom ones. Moreover, derivation modes cannot be user-defined, i.e, the way in which P system computations should be generated is determined by the simulation algorithm in the source code. The main contribution of this paper is a completely new design of the P-Lingua language, called P-Lingua 5, in which the user can define custom variants and derivation modes, among other improvements such as including procedural programming and simulation directives. It is worth mentioning that it has backward-compatibility with previous versions of the language. A completely new set of command-line tools is provided for parsing and simulating P-Lingua 5 files. Finally, several examples are included in this paper covering the most common P system types. [ABSTRACT FROM AUTHOR]

A complex dynamical network (CDN) can be considered as the composition system with the nodes subsystem (NS) and the links subsystem (LS), and both subsystems are coupled with each other. Therefore, the dynamics of NS affects the dynamics of LS, and vice versa. In this paper, two vector differential equation (VDE)s are employed to describe the dynamics of NS and LS, respectively, in which the dynamics of NS is proposed as the VDE with the second derivative term (SDT) for more realistic engineering applications. Compared with the existing literature, the key advantage is that the dynamics of links is utilized to assist synthesizing the tracking controller of NS. The results show that when the state of LS tracks asymptotically the synthesized auxiliary tracking goal (ATG), the state of NS tracks asymptotically the given reference signal. Observing the eventual topology of CDN, all eventual links between nodes depend on the proposed ATG when NS achieving the tracking target, in which one special case is that if all target signals determined by ATG are not zero, all nodes are not isolated. Finally, the effectiveness of the proposed control scheme is verified by a numerical simulation example. [ABSTRACT FROM AUTHOR]

The topic of optimal antisynchronization control for unknown multiagent systems (MASs) with cooperative-competitive (i.e.,coopetition) interaction is challenging because of the complex connection characteristics and the coupling among agents. This paper proposes a reinforcement learning Algorithm based on coopetition strength (CS) to achieve optimal antisynchronization in unknown MASs. Firstly, an innovative CS function is explored, and the local state error information of the agents can be redefined. Furthermore, we propose a novel strategy iteration method to approximate the agent's optimal control policy. Meanwhile, the proposed algorithm's convergence analysis is presented, which is based on the Lyapunov stability and functional theorem. In the implementation of a data-based control policy, a network structure of actor-critic (AC) is designed. To improve the robustness of the control policy, the target network and experience replay (ER) are introduced in the training process. Finally, the algorithm's effectiveness is validated using comparable numerical simulations. [ABSTRACT FROM AUTHOR]

Competition is considered to be a driving force of many swarm systems in maintaining vitality, as important as collaboration. To model this competitive nature, an operation called k -winner-take-all (k WTA) is introduced that can output k maximum values from p input signals with 1 ⩽ k ⩽ p. In this paper, different projection functions (PFs) are combined with k WTA operations as activation functions for the first time, and a P- k WTA network is proposed, analyzed, and applied, which accelerates the convergence rate and enhances the robustness of existing models. With the aid of various characteristics, such as saturated or nonconvex, the convergent process of the proposed P- k WTA network is able to present diverse effects of PFs. Additionally, numerical simulations, an application to a multi-agent system, and an experiment of multiple E-puck robots on the CoppeliaSim platform all demonstrate the feasibility and effectiveness of the P- k WTA network. [ABSTRACT FROM AUTHOR]

This paper studies the discrete-time multiagent consensus problem with kinds of diverse interaction distortions which are related to the states of agents, and a novel dual switching control strategy is proposed, named echo control, to make the system achieve state consensus. The main feature of the echo control strategy is that agents resend the information flows (received from neighbors) to the corresponding neighbor, just like the reflecting of sound waves. In other words, every individual under the echo control strategy is not only the sender and receiver of the information flows, but also the reflector of its neighbors' messages. In this way, a negative feedback loop is constructed between every two agents, which is designed to ensure the stability of the multiagent system (MAS), and then the agents' states will converge to a common value. The effectiveness of the echo control protocol is theoretically analyzed, and numerical simulations validate the correctness of the relevant results. [ABSTRACT FROM AUTHOR]

This paper deals with the fixed-time stabilization (FXTS) and preassigned-time stabilization (PATS) problems for delayed memristive neural networks (DMNNs) via a unified controller. Firstly, we design a delayed controller to realize the FXTS of DMNNs. Moreover, the sufficient conditions and accurate time estimation of FXTS are presented. It is proved that the system states can achieve stabilization within a fixed time without being affected by the initial states. Then, by modifying the parameters of the same controller, DMMNs achieve stabilization within an arbitrary preassigned time, which gets rid of the limitation of system and controller parameters. Finally, the feasibility and validity of the main results are verified by numerical simulations. [ABSTRACT FROM AUTHOR]

This paper investigates continuous-time complex dynamical networks (CDNs) with dynamic connection relationships. The CDNs are regarded as interconnected systems composed of intercoupled subsystems of links and nodes. Different from previous research, a simplified and intuitive vector dynamic model is employed to describe the links subsystem (LS) rather than a matrix equation. Because the state of the links cannot be measured accurately in practice, the stabilization and synchronization of the nodes subsystem (NS) are investigated via the auxiliary role of the LS. Using the proposed node controllers and coupling forms in the LS, the CDNs can be stabilized and synchronized. Finally, numerical simulations are presented to verify the theoretical results. [ABSTRACT FROM AUTHOR]

This study addresses the problem of observer design and its applications to attack detection for an interconnected cyber-physical system subjected to unknown disturbances and sensor attacks. First, an overall system is constructed using the information on the interconnection of several subsystems, and problems related to the observer design are then solved. Second, to facilitate the residual's sensitivity to attacks and its robustness against unknown disturbances, an observer is provided. The gain matrix is developed using both the H − performance and mixed L 2 − L ∞ / H ∞ performance. Third, for the suppression of the effect of unknown disturbances and attack signals on the errors in the state estimation and on attack detection in a finite-frequency domain, the generalized Kalman-Yakubovich-Popov lemma is applied to set the conditions under which the observer can operate effectively. In light of the detection scheme, we suggest a detection logic that prevents false alarms by comparing the evaluation function to the corresponding threshold. Additionally, an interval threshold-based method is introduced to establish the threshold bounds, and numerical simulation results are provided to demonstrate the method's validity in this paper. [ABSTRACT FROM AUTHOR]

In this paper, the exponential synchronization of multilayer neural networks (MNNs) is investigated via alternate periodic event-triggered control (APETC). Distinguished from the previous work, a novel APETC which incorporates aperiodically intermittent control (AIC) and periodic event-triggered mechanism is firstly proposed. Determined by two event-triggered conditions, the control and rest intervals of APETC are based on the present state of the system rather than being predetermined. In contrast to the conventional event-triggered control (ETC), the event-triggered conditions of APETC can not only judge the updates of control signals, but also dominate the actuation and close of the controller. Moreover, by introducing the sampling period into ETC, the number of event triggers can be decreased and the Zeno phenomenon is completely avoided. Subsequently, synchronization criteria for MNNs under APETC are established on the basis of Lyapunov method and graph theory. Finally, several numerical simulations are performed to demonstrate the validity of the theoretical results. [ABSTRACT FROM AUTHOR]

It is widely acknowledged that the initial spreaders play an important role in the spread of information in complex networks. Thus, a variety of centrality-based methods have been proposed for identifying the most influential spreaders. However, most existing studies overlook the fact that, in real social networks, it is more costly and difficult to convince influential individuals to act as initial spreaders, resulting in a high risk to maximal spreading. In this paper, we address this problem on the basis of the assumption that the activation of large-degree nodes carries a higher risk than that of small-degree nodes. We aim to identify the initial spreaders that most effectively maximize the spreading when considering both the activation risk and the outbreak size of the initial spreaders. Analysis of random networks reveals that the degree of the optimal initial spreaders does not correspond to the largest node degree in the network, but is instead determined by the infection probability and difference in activation risk among nodes with different degrees. We propose a risk-aware metric to identify the most effective spreaders in real networks. Numerical simulations show that this risk-aware metric outperforms the existing benchmark centralities in terms of maximizing the spreading. [ABSTRACT FROM AUTHOR]

• The PIR protocol is improved using multiple intentional delays as tunable parameters for second-order multi-agent systems. • A systematic and flexible parameter tuning strategy is presented for our proposed PIR protocol. • The superiority of our PIR protocol is demonstrated by developing a comprehensive comparison. • Our PIR protocol is superior in noise attenuation over the PID scheme. • Our PIR protocol outperforms the PR protocol regarding consensus speed, parameter robustness, and disturbance resistance. The attractive characteristics of an innovative delay-based controller called Proportional-Integral-Retarded (PIR) controller are reported in many fields. However, a detailed investigation of the merits of the PIR controller for multi-agent systems (MASs) is still missing. To bridge this gap, we propose an improved PIR protocol for a general class of second-order MASs. This protocol, using multiple intentional delays and heterogeneous gains as tunable parameters, realizes the optimal spectrum assignment of each subsystem in a completely independent way without affecting the stability of other subsystems. We then present a systematic and flexible parameter tuning strategy for the PIR protocol such that the desired exponential decay rate of the consensus system can be achieved. Specifically, this strategy achieves an arbitrary dominant root assignment in the domain of non-negative real numbers and enables enhanced control flexibility by adjusting an additionally introduced free variable in the analytical parameter formulae. To unveil the superiority of our proposed PIR protocol, we develop a comprehensive comparison of the PIR protocol with the Proportional-Integral-Derivative (PID) scheme and the Proportional-Retarded (PR) protocol. The numerical simulations show that our PIR protocol outperforms the PID scheme regarding the noise attenuation property. Besides, this protocol can attain faster consensus, stronger robustness against parameter uncertainties, and superior disturbance resistance than the PR protocol. Our paper provides a valuable reference for the design of an effective and implementable multi-agent consensus protocol. [ABSTRACT FROM AUTHOR]

In the face of an emergency, regionally coordinated allocation is an important prerequisite for maintaining the normal order of production and living. Considering the complexity and uncertainty of the emergencies in local governments, this paper establishes a two-stage process for allocating medical resources. In the first stage, cooperative regions with incomplete weights and multidimensional uncertain information ranked via a novel decision-making method. The second stage is an optimal strategy which the optimization model is established to minimize the cost incurred by the local government considering two components of cost. The first stage is the reserve cost for the local government to prepare a certain amount of flexible procurement materials to respond to a public health emergency. The second is the scheduling cost when cooperative regions support medical resources. Theoretically, the optimal allocation of the reserve of different kinds of medical resources is deduced at the lowest cost. Through numerical simulation and sensitivity analysis, we explore the impacts of attribute weights, resource reserve capacity, unit costs, and the number of cooperative regions on the demand for different kinds of medical resources and the total costs incurred by local governments. This study provides a regional coordinated allocation framework and theoretical reference for government departments responding to the emergencies. [ABSTRACT FROM AUTHOR]

This paper studies passivity analysis and stability analysis for neural networks with time-variant delay. The time-variant delay is presumed to respond in trigonometric form. Firstly, a novel interval approximation method is constructed with adjustable parameters, which can be adjusted to reduce conservatism. According to the feature of time delay in trigonometric form, the specific allowable delay set can be obtained. Secondly, by introducing the delay-product-type parts in Lyapunov-Krasovskii functional (LKF), the emphatically improved passivity criterion and stability criterion with less conservatism are obtained by using the advanced inequalities. Finally, two numerical simulations are listed where our work can obtain larger maximum allowable delay bounds compared with other works, which demonstrate that the results based on the interval approximation method are less conservative. [ABSTRACT FROM AUTHOR]

This paper pays attention to investigating the exponential stability of stochastic multi-layer complex network with regime-switching diffusion (SMLCNRSD). Different from the existing stability results on stochastic complex network, what we research is to consider the regularity of the solution process under the local conditions, and make use of the truncation method to obtain the global existence and uniqueness of the solution. Using graph theory, Lyapunov method, as well as some stochastic analysis techniques, several sufficient criteria for exponential stability are attained by aperiodically intermittent control. Finally, the theoretical results are applied to study the exponential stability of a two-layer Hindmarsh-Rose neuron network with regime-switching diffusion. Moreover, the effectiveness of the results provided has been well demonstrated through numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, the memory property and the historical dynamic information of a fractional system via event-triggered control are studied. A unit step function is introduced and the control input is taken as a piecewise function. By theorem analysis and numerical simulations, it is shown that the fractional calculus of a piecewise function is relevant to the entire historical dynamic information and cannot be calculated in segments because of its memory property. So, the state of a fractional system via event-triggered control is affected by all input from the initial time, but not the triggering time, to the current time. But in previous studies, this property is neglected and the historical dynamic information has not been fully studied, which disagrees with the real physical systems. Therefore, the historical dynamic information of a fractional system via event-triggered control should be studied in order to satisfy the demands in engineering. [ABSTRACT FROM AUTHOR]

This paper devotes to solving time-varying linear matrix equations (TVLMEs) from the viewpoint of high-order neural networks. For this purpose, high-order zeroing neural network (ZNN) models are designed and studied to solve TVLMEs. Compared with the first-order ZNN model for TVLMEs, the proposed high-order ZNN models are based on the design of the high-order error functions, and different order choices will generate different high-order ZNN models. Two nonlinear activation functions [i.e., tunable activation function (TunAF) and sign-bi-power activation function (SBPAF)] are used to speedup the high-order ZNN models for achieving the finite-time convergence. Furthermore, the strict theoretical analyses are provided to show that high-order ZNN models have better properties (especially in terms of convergence), when the nonlinear activation functions are used. Two numerical simulations are given to reveal the superior convergence property of the proposed high-order ZNN models, as compared to the first-order ZNN model for solving TVLMEs. [ABSTRACT FROM AUTHOR]

The secure message recovery problem in presence of cyber-attack is considered in this paper. The message is modulated by a master chaotic system which may be vulnerable to a cyber-attack and then transmitted to a receiver. By designing a novel observer at the receiver side, the message is recovered correctly. All the design process is performed in discrete-time domain which is suitable for digital communications. Besides, there are no restrictions on the message signal and nonlinear term signature matrix which makes the proposed approach more suitable in the real applications. Numerical simulations are introduced to show the feasibility and the superior performance of the proposed scheme in comparison with the conventional methods. [ABSTRACT FROM AUTHOR]

Effectively measuring the information content of Basic Probability Assignments (BPA) is a crucial prerequisite for addressing uncertain information within the framework of Dempster-Shafer theory. In previous research, uncertainty and dissimilarity measures for BPAs were often treated separately to counteract the impact of incomplete mutual exclusion between focal elements. In this paper, we introduce a Transient Mass Function (TMF) based on the process of pignistic probability transformation to forge a link between probabilistic and evidential information. As a transient state of BPA, the TMF not only considers the structural features of the focal element but also maintains its numerical content. Carrying out probabilistic information measures on the TMF is equivalent to performing belief information measures on the original BPA. Finally, validated by numerical simulations, TMF provides a unified and effective metric framework for evidential information. [ABSTRACT FROM AUTHOR]

Most transfer learning (TL) models generally need the fault data from similar scenarios to achieve cross-domain bearing fault diagnosis. However, due to the bearings are mostly in normal state and the fault experiment cost is high, it is hard to collect the complete fault data in any real scenario. Thus, the problem of no fault data still limits the application of various intelligent diagnosis methods, including TL methods. To solve this problem, this paper proposed a novel transfer learning (TL) strategy by driving the one-dimensional (1D) cycle-consistent generative adversarial network (Cycle-GAN) with numerical simulation. In this strategy, the bearing dynamic model is constructed to generate the simulated vibration signals under normal and fault states. Furthermore, a 1D Cycle-GAN is first devised as the TL model for signal-to-signal translation. By using all simulated signals (normal and fault) and real normal signals, this 1D Cycle-GAN is trained to translate each simulated signal into a nearly real signal. Two experiments indicate that this strategy can generate satisfactory fault signals to solve the problem of no fault data in bearing fault diagnosis. [ABSTRACT FROM AUTHOR]