Fixed-Time Synchronization of Coupled Neural Networks With Discontinuous Activation and Mismatched Parameters

Selection and optimization of drive nodes in drive-response networks

This paper considers the selection and optimization of drive nodes based on the controllability of multilayer networks. The intra-layer network topologies are arbitrary, and the node dynamics are linear time-invariant dynamical systems. The study focuses on the number and selection of drive nodes in a special class of drive-response networks. Several conclusions are drawn through the investigation: (1) All the drive nodes cannot be placed in the response layer but can be contained in the drive layer; (2) The minimum number of drive nodes placed in the drive layer is equal to the maximum geometric multiplicity of the system matrix of the drive layer; (3) The configuration of interlayer coupling weight significantly affects the number and distribution of drive nodes. Moreover, an optimization scheme is proposed based on the Gershgorin circle theorem, which aims to minimize the number of drive nodes in the entire network. This scheme ensures that regardless of the drive nodes originally needed, they can be reduced to the maximum geometric multiplicity of the system matrix of the drive layer. Numerical simulations on a general two-layer network as well as various synthetic networks are provided to validate the results.

Improved fixed-time stability analysis and applications to synchronization of discontinuous complex-valued fuzzy cellular neural networks

This article mainly centers on proposing new fixed-time (FXT) stability lemmas of discontinuous systems, in which novel optimization approaches are utilized and more relaxed conditions are required. The conventional discussions about Vt>1 and 0 Collapse

Key Words

• Cellular neural networks
• Complex-valued neural networks
• Fixed-time synchronization
• Fuzzy neural networks
• Non-separation approach

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MESH Headings

• Neural Networks, Computer
• Fuzzy Logic
• Computer Simulation
• Algorithms
• Time Factors

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Affiliation(s)

Jingsha Zhang Hebei Provincial Innovation Center for Wireless Sensor Network Data Application Technology, Hebei Provincial Key Laboratory of Information Fusion and Intelligent Control, Hebei Normal University, Shijiazhuang 050024, China.
Jing Yang Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang 050003, China.
Qintao Gan Shijiazhuang Campus, Army Engineering University of PLA, Shijiazhuang 050003, China.
Huaiqin Wu School of Science, Yanshan University, Qinhuangdao 066001, China.
Jinde Cao School of Mathematics, Southeast University, Nanjing 210096, China; Yonsei Frontier Lab, Yonsei University, Seoul 03722, South Korea.

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Mode-Mixed Effects Based Intralayer-Dependent Impulsive Synchronization for Multiple Mismatched Multilayer Neural Networks

This article focuses on the intralayer-dependent impulsive synchronization of multiple mismatched multilayer neural networks (NNs) with mode-mixed effects. Initially, a novel multilayer NN model that removes the one-to-one interlayer coupling constraint and introduces nonidentical model parameters is first established to meet diverse modeling requirements in complex applications. To help the multilayer target NNs with mismatched connection coefficients and time delays achieve synchronization, the hybrid controller is designed using intralayer-dependent impulsive control and switched feedback control approaches. Furthermore, the mode-mixed effects caused by the intralayer coupling delays and switched intralayer topologies are incorporated into the novel model and analysis method to ensure that the subsystems operating within the current switching interval can effectively use the topology information of the previous switching intervals. Then, a novel analysis framework including super-Laplacian matrix, augmented matrix, and mode-mixed methods is developed to derive the synchronization results. Finally, the main results are verified via the numerical simulation with secure communication.

Quasi-synchronization for variable-order fractional complex dynamical networks with hybrid delay-dependent impulses

This paper focuses on addressing the problem of quasi-synchronization in heterogeneous variable-order fractional complex dynamical networks (VFCDNs) with hybrid delay-dependent impulses. Firstly, a mathematics model of VFCDNs with short memory is established under multi-weighted networks and mismatched parameters, which is more diverse and practical. Secondly, under the framework of variable-order fractional derivative, a novel fractional differential inequality has been proposed to handle the issue of quasi-synchronization with hybrid delay-dependent impulses. Additionally, the quasi-synchronization criterion for VFCDNs is developed using differential inclusion theory and Lyapunov method. Finally, the practicality and feasibility of this theoretical analysis are demonstrated through numerical examples.

Tradeoff analysis between time cost and energy cost for fixed-time synchronization of discontinuous neural networks

This article focuses on the tradeoff analysis between time and energy costs for fixed-time synchronization (FXTS) of discontinuous neural networks (DNNs) with time-varying delays and mismatched parameters. First, a more comprehensive lemma is systematically established to study fixed-time stability, which is less conservative than those in most current results. Besides, theoretical proof has proven that the upper bounds of the settling time (ST) in this article are more accurate compared to existing results. Second, on the grounds of the new fixed-time stability lemma, fixed-time synchronization problem for discontinuous neural networks with time-varying delays and mismatched parameters is explored, and sufficient conditions for fixed-time synchronization are obtained. Further, the upper bounds of energy cost during the synchronization process are estimated. Third, in order to achieve a balance between time cost and energy cost, the genetic algorithm is utilized to find the satisfactory control parameter. Finally, a numerical example is provided to verify the theoretical analysis's correctness and the control mechanism's feasibility.

Event-triggered impulsive cluster synchronization of coupled reaction-diffusion neural networks and its application to image encryption

This paper investigates the cluster synchronization of coupled neural networks with reaction-diffusion terms. With the help of impulsive control strategies, some cluster synchronization criteria are proposed by an appropriate event-triggered mechanism. A numerical example is given to verify the validity of the theoretical results. Additionally, the proposed event-triggered impulsive synchronization is successfully applied to image encryption with encouraging cryptanalysis results demonstrating its strong ability to efficiently encrypt images.

Finite-Time Synchronization and H∞ Synchronization for Coupled Neural Networks With Multistate or Multiderivative Couplings

This article investigates the finite-time synchronization (FTS) and H∞ synchronization for two types of coupled neural networks (CNNs), that is, the cases with multistate couplings and with multiderivative couplings. By designing appropriate state feedback controllers and parameter adjustment strategies, some FTS and finite-time H∞ synchronization criteria for CNNs with multistate couplings are derived. In addition, we further consider the FTS and finite-time H∞ synchronization problems for CNNs with multiderivative couplings by utilizing state feedback control approach and selecting suitable parameter adjustment schemes. Finally, two simulation examples are given to demonstrate the effectiveness of the proposed criteria.

Interval Bipartite Synchronization of Multiple Neural Networks in Signed Graphs

Interval bipartite consensus of multiagents described by signed graphs has received extensive concern recently, and the rooted cycles play a critical role in stabilization, while the structurally balanced graphs are essential to achieve bipartite consensus. However, the gauge transformation used in the linear system is no longer feasible in the nonlinear case. This article addresses interval bipartite synchronization of multiple neural networks (NNs) in a signed graph via a Lyapunov-based approach, extending the existing work to a more practical but complicated case. A general matrix M in signed graphs is introduced to construct the novel Lyapunov functions, and sufficient conditions are obtained. We find that the rooted cycles and the structurally balanced graphs are essential to stabilize and achieve bipartite synchronization. More importantly, we discover that the nonrooted cycles are crucial in reaching interval bipartite synchronization, not previously mentioned. Several examples are presented to illustrate interval bipartite synchronization of multiple NNs with signed graphs.

Adaptive Exponential Synchronization of Complex Networks With Nondifferentiable Time-Varying Delay

In recent years, the adaptive exponential synchronization (AES) problem of delayed complex networks has been extensively studied. Existing results rely heavily on assuming the differentiability of the time-varying delay, which is not easy to verify in reality. Dealing with nondifferentiable delay in the field of AES is still a challenging problem. In this brief, the AES problem of complex networks with general time-varying delay is addressed, especially when the delay is nondifferentiable. A delay differential inequality is proposed to deal with the exponential stability of delayed nonlinear systems, which is more general than the widely used Halanay inequality. Next, the boundedness of the adaptive control gain is theoretically proved, which is neglected in much of the literature. Then, the AES criteria for networks with general delay are established for the first time by using the proposed inequality and the boundedness of the control gain. Finally, an example is given to demonstrate the effectiveness of the theoretical results.

Predefined-Time Bounded Consensus of Multiagent Systems With Unknown Nonlinearity via Distributed Adaptive Fuzzy Control

This article investigates uniformly predefined-time bounded consensus of leader-following multiagent systems (MASs) with unknown system nonlinearity and external disturbance via distributed adaptive fuzzy control. First, uniformly predefined-time-bounded stability is analyzed and a sufficient condition is derived for the system to achieve semiglobally (globally) uniformly predefined-time-bounded consensus. Therein, the settling time is independent of initial conditions and can be defined in advance. Then, for first-order MASs, distributed adaptive fuzzy controllers are designed by combining neighboring consensus errors to drive all following agents to globally track the leader's state within predefined time. For second-order MASs, by formulating filtered errors, the consensus errors between following agents and the leader are shown to be bounded if the filtered errors are bounded. Furthermore, with the distributed controllers designed based on filtered errors, second-order MASs achieve semiglobally uniformly predefined-time-bounded leader-following consensus. Finally, two numerical examples are simulated, including: 1) a first-order leader-following MAS and 2) a second-order Lagrangian system consisting of single-link manipulators, to demonstrate the performance of the proposed controllers.

Predefined-time synchronization of coupled neural networks with switching parameters and disturbed by Brownian motion

This article focuses on predefined time synchronization problem for a class of signal switching neural networks with time-varying delays. In the network models, we not only consider the coupling characteristics in the following networks, but also consider the disturbance with standard Brownian motion. In the design of the controller, the control gain is designed as 1ɛ+T_p-t (t∈[T₀,T_p), ɛ is an optional smaller positive number), which avoids the infinite gain (the control gain is designed as 1T_p-t in other reference). In order to get the predefined time control law, a power function is multiplied to the Lyapunov functional, from which it can get an exponential upper bound function via the derivative and mathematical expectation operation. Utilizing the martingale theory and the method of Laplace matrix, some novel predefined time synchronization criteria are obtained for the leader-following neural networks, meanwhile the following networks can maintain the leader network after achieved synchronization. Based on the special network of the main system, five corollaries separately develop the predefined time synchronization results from different perspectives. An example with some simulation figures and computing results fully exhibits the effectiveness of the achieved synchronization scheme. In this case, although the error signal is disturbed by Brownian motion, the trace signal can still stably converge to zero by this control scheme, meanwhile the predefined-time control effect is achieved.

Adaptive fixed-time output synchronization for complex dynamical networks with multi-weights

This paper addresses fixed-time output synchronization problems for two types of complex dynamical networks with multi-weights (CDNMWs) by using two types of adaptive control methods. Firstly, complex dynamical networks with multiple state and output couplings are respectively presented. Secondly, several fixed-time output synchronization criteria for these two networks are formulated based on Lyapunov functional and inequality techniques. Thirdly, by employing two types of adaptive control methods, fixed-time output synchronization issues of these two networks are dealt with. At last, the analytical results are verified by two numerical simulations.

Maximizing synchronizability of networks with community structure based on node similarity

In reality, numerous networks have a community structure characterized by dense intra-community connections and sparse inter-community connections. In this article, strategies are proposed to enhance synchronizability of such networks by rewiring a certain number of inter-community links, where the research scope is complete synchronization on undirected and diffusively coupled dynamic networks. First, we explore the effect of adding links between unconnected nodes with different similarity levels on network synchronizability and find that preferentially adding links between nodes with lower similarity can improve network synchronizability more than that with higher similarity, where node similarity is measured by our improved Asymmetric Katz (AKatz) and Asymmetric Leicht-Holme-Newman (ALHNII) methods from the perspective of link prediction. Additional simulations demonstrate that the node similarity-based link-addition strategy is more effective in enhancing network synchronizability than the node centrality-based methods. Furthermore, we apply the node similarity-based link-addition or deletion strategy as the valid criteria to the rewiring process of inter-community links and then propose a Node Similarity-Based Rewiring Optimization (NSBRO) algorithm, where the optimization process is realized by a modified simulated annealing technique. Simulations show that our proposed method performs better in optimizing synchronization of such networks compared with other centrality-based heuristic methods. Finally, simulations on the Rössler system indicate that the network structure optimized by the NSBRO algorithm also leads to better synchronizability of coupled oscillators.

A model for analyzing competitive dynamics on triplex networks

This paper studies the evolution process of competitive dynamics on triplex complex networks. We propose a new triplex network model in which the state of the node in each layer is affected by its neighbors as well as inter-layer competition. Through this model, we combine the opinion diffusion model, the Ising model, and the signed network and extend their application from single-layer to multi-layer networks. We derive the evolution process and dynamical equations of the model and carry out a series of numerical simulations to discuss the influence of several factors on the evolution process and the competitiveness of the network. First, we find that the increase of global transition threshold p or the proportion of initial active nodes will lead to more surviving layers and more active nodes in each layer. In addition, we summarize the similarities and differences of the evolution curves under different conditions. Second, we discuss the influence of initial active nodes and the average degree on the competitiveness of the network and find the correlations between them. Finally, we study the relationship between network topology and network competitiveness and conclude the conditions for the best competitiveness of the network. Based on the simulation results, we give specific suggestions on how to improve the competitiveness of the platform in reality.

Synchronizability of double-layer dumbbell networks

Synchronization of multiplex networks has been a topical issue in network science. Dumbbell networks are very typical structures in complex networks which are distinguished from both regular star networks and general community structures, whereas the synchronous dynamics of a double-layer dumbbell network relies on the interlink patterns between layers. In this paper, two kinds of double-layer dumbbell networks are defined according to different interlayer coupling patterns: one with the single-link coupling pattern between layers and the other with the two-link coupling pattern between layers. Furthermore, the largest and smallest nonzero eigenvalues of the Laplacian matrix are calculated analytically and numerically for the single-link coupling pattern and also obtained numerically for the two-link coupling pattern so as to characterize the synchronizability of double-layer dumbbell networks. It is shown that interlayer coupling patterns have a significant impact on the synchronizability of multiplex systems. Finally, a numerical example is provided to verify the effectiveness of theoretical analysis. Our findings can facilitate company managers to select optimal interlayer coupling patterns and to assign proper parameters in terms of improving the efficiency and reducing losses of the whole team.

Co-evolution spreading of multiple information and epidemics on two-layered networks under the influence of mass media

During epidemic outbreaks, there are various types of information about epidemic prevention disseminated simultaneously among the population. Meanwhile, the mass media also scrambles to report the information related to the epidemic. Inspired by these phenomena, we devise a model to discuss the dynamical characteristics of the co-evolution spreading of multiple information and epidemic under the influence of mass media. We construct the co-evolution model under the framework of two-layered networks and gain the dynamical equations and epidemic critical point with the help of the micro-Markov chain approach. The expression of epidemic critical point show that the positive and negative information have a direct impact on the epidemic critical point. Moreover, the mass media can indirectly affect the epidemic size and epidemic critical point through their interference with the dissemination of epidemic-relevant information. Though extensive numerical experiments, we examine the accuracy of the dynamical equations and expression of the epidemic critical point, showing that the dynamical characteristics of co-evolution spreading can be well described by the dynamic equations and the epidemic critical point is able to be accurately calculated by the derived expression. The experimental results demonstrate that accelerating positive information dissemination and enhancing the propaganda intensity of mass media can efficaciously restrain the epidemic spreading. Interestingly, the way to accelerate the dissemination of negative information can also alleviate the epidemic to a certain extent when the positive information hardly spreads. Current results can provide some useful clues for epidemic prevention and control on the basis of epidemic-relevant information dissemination.