具有多重权值的时滞复杂网络固定时间同步问题研究

文章研究了基于非周期间歇性控制的具有多重权值和耦合时滞的复杂网络固定时间同步问题.通过构建具有多重权值的复杂网络模型,并基于固定时间稳定性引理和矩阵理论,给出了实现复杂网络固定时间同步的充分条件.此外,文章设计了固定时间非周期切换控制器,获得了实现复杂网络同步的时间上界的估计值.结论证明了实现网络同步的时间与网络的初始状态无关,最后数值模拟说明了理论结果的正确性和有效性.     

Intermittent impulsive projective synchronization in time‐varying delayed dynamical network with variable structures

This paper studies the projective synchronization behavior in a drive‐response dynamical network with coupling time‐varying delay via intermittent impulsive control. Different from the most publications on drive‐response dynamical networks under the general impulsive control, here the impulsive effects can only exist at control windows, not during the whole time. Moreover, intermittent impulsive control does not need the limitation of the upper bound of the impulsive intervals. By utilizing the Lyapunov‐Razumikhin technique, some sufficient conditions for the projective synchronization are derived. Numerical simulations are provided to verify the correctness and effectiveness of the proposed method and results. © 2016 Wiley Periodicals, Inc. Complexity 21: 547–556, 2016     

Hybrid Synchronization of two complex delayed dynamical networks with nonidentical topologies and mixed coupling

In this article, we study a new hybrid synchronization scheme for two different delayed dynamical networks with nonidentical topologies and mixed coupling. Based on Barbalat lemma and Schur complement lemma, some hybrid synchronization criteria are achieved via the open‐loop‐plus‐pinning adaptive control strategy. Two numerical examples with two types of node dynamics illustrate the effectiveness of the proposed synchronous criteria. © 2016 Wiley Periodicals, Inc. Complexity 21: 470–482, 2016     

Synchronization analysis of networks with both delayed and non-delayed couplings via adaptive pinning control method

In this paper, simple controllers are designed to realize the synchronization of complex networks with time delays, in which the coupling configuration matrix and inner coupling matrix are not restricted to be symmetric matrix. Several adaptive synchronization criteria are obtained based on Lyapunov stability theory. These criteria relay on the coupling strength and the number of nodes pinning to the networks. For a given complex dynamical network with both delayed and non-delayed couplings, we give the minimum number of controllers under which synchronization can be achieved. One example shows the effectiveness of the proposed pinning adaptive controller.     

Adaptive cluster synchronization in directed networks with nonidentical nonlinear dynamics

In this article, the problem of cluster synchronization in the complex networks with nonidentical nonlinear dynamics is considered. By Lyapunov functional and M‐matrix theory, some sufficient conditions for cluster synchronization are obtained. Moreover, the least number of nodes which should be pinned is given. It is shown that when the root nodes of all the clusters are pinning‐controlled, cluster synchronization with adaptive coupling strength can be achieved. Different from the constraints of many literatures, the assumption is that each row sum for all diagonal submatrices of the Laplacian matrix is equal to zero. Finally, a numerical simulation in the network with three scale‐free subnetwork is provided to demonstrate the effectiveness of the theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 380–387, 2016     

Further results on the impulsive synchronization of uncertain complex‐variable chaotic delayed systems

Synchronization and control of nonlinear dynamical systems with complex variables has attracted much more attention in various fields of science and engineering. In this article, we investigate the problem of impulsive synchronization for the complex‐variable delayed chaotic systems with parameters perturbation and unknown parameters in which the time delay is also included in the impulsive moment. Based on the theories of adaptive control and impulsive control, synchronization schemes are designed to make a class of complex‐variable chaotic delayed systems asymptotically synchronized, and unknown parameters are identified simultaneously in the process of synchronization. Sufficient conditions are derived to synchronize the complex‐variable chaotic systems include delayed impulses. To illustrate the effectiveness of the proposed schemes, several numerical examples are given. © 2014 Wiley Periodicals, Inc. Complexity 21: 131–142, 2016     

A novel criterion for cluster synchronization of complex dynamical networks with coupling time-varying delays

This paper investigates the cluster synchronization problem for the time-varying delays coupling networks with nonidentical delayed dynamical systems by using pinning control method. We derive some simple and useful criteria for cluster synchronization for any initial values through an effective feedback control scheme and propose an adaptive feedback strategy that adjusts automatically the coupling strength. Finally, some numerical examples are then given to illustrate the theoretical results.     

Robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties

The problem of robust decentralized adaptive synchronization of general complex networks with coupling delayed and uncertainties is investigated in this article. It is only assumed that the upper normal bound of uncertain inner and outer coupling matrices is positive but its concrete structure is not also required to be known. The time‐varying coupling delay is a any nonnegative continuous and bounded function and not require its derivative to be less than one, that is, general time‐varying coupling delays and uncertainties. For such a class of uncertain complex networks, a new synchronization scheme is presented by a class of continuous memoryless robust decentralized adaptive synchronization controllers. It is also shown that the synchronization error dynamics of uncertain complex networks can be guaranteed as uniformly exponentially convergent toward a ball that can be as small as desired. Finally, numerical simulations are provided to demonstrate the effectiveness and robustness of proposed complex networks synchronization schemes. © 2013 Wiley Periodicals, Inc. Complexity 19: 10–26, 2014     

Synchronization for stochastic hybrid coupled controlled systems with Lévy noise

In this paper, synchronization for stochastic hybrid-delayed coupled systems with Lévy noise on a network (SHDCLN) is investigated via aperiodically intermittent control. Here time delays, Markovian switching and Lévy noise are considered on a network simultaneously for the first time. After that, by means of Lyapunov method, graph theory, and some techniques of inequality, some sufficient conditions are derived to guarantee the synchronization for SHDCLN. In addition, the designed range of aperiodically intermittent controller parameters is shown. Meanwhile, the coupling strength and the perturbed intensity of noise have a great impact on the intensity of control. Then, we investigate synchronization for stochastic hybrid delayed Chua's circuits with Lévy noise on a network as a practical application of our theoretical results. Finally, a numerical example is given to illustrate the effectiveness of the theoretical results.     

Finite‐Time lag synchronization of delayed neural networks via periodically intermittent control

The problem of finite‐time lag synchronization of delayed neural networks via periodically intermittent control is studied. In two sections, based on the same finite‐time stability theory and using the same sliding mode control, by designing a periodically intermittent feedback controller and adjusting periodically intermittent control strengths with the updated laws, we achieve the finite‐time lag synchronization between two time delayed networks. In addition, we ensure that the trajectory of the error system converges to a chosen sliding surface within finite time and keeps it on forever. Finally, two examples are presented to verify the effectiveness of the analytical results obtained here. © 2015 Wiley Periodicals, Inc. Complexity 21: 211–219, 2016     

Pinning impulsive synchronization of complex dynamical networks with various time-varying delay sizes

This paper studies the pinning impulsive synchronization problem for a class of complex dynamical networks with time-varying delay. By applying the Lyapunov stability theory and mathematical analysis technique, sufficient verifiable criterion for the synchronization of delayed complex dynamical networks with small delay is derived analytically. It is shown that synchronization can be achieved by only impulsively controlling a small fraction of network nodes. Moreover, a novel sufficient condition is constructed to relax the restrictions on the size of time-delay and guarantee the synchronization of concerned networks with large delay. Two numerical examples are presented to illustrate the effectiveness of the obtained results.     

Robust adaptive synchronization of uncertain complex networks with multiple time‐varying coupled delays

In this article, the synchronization problem of uncertain complex networks with multiple coupled time‐varying delays is studied. The synchronization criterion is deduced for complex dynamical networks with multiple different time‐varying coupling delays and uncertainties, based on Lyapunov stability theory and robust adaptive principle. By designing suitable robust adaptive synchronization controllers that have strong robustness against the uncertainties in coupling matrices, the all nodes states of complex networks globally asymptotically synchronize to a desired synchronization state. The numerical simulations are given to show the feasibility and effectiveness of theoretical results. © 2014 Wiley Periodicals, Inc. Complexity 20: 62–73, 2015     

Stabilization of novel multi-layer networks with noise-based nonlinear superior couplings via aperiodically adaptive intermittent pinning control

In this paper, novel multi-layer networks with superior couplings are proposed firstly which are established on a non-strongly connected digraph. Within the multi-layer networks, a nonlinear coupling based on white noises is introduced, which is the feature of superior couplings. We adopt aperiodically adaptive intermittent pinning control to stabilize the multi-layer networks. An concrete analysis framework about selecting the target vertex of the control is revealed. Aperiodically adaptive intermittent control is employed on the vertex systems of the first layer networks, to achieve the stabilization of the first layer networks, where the couplings of drift terms are treated as negative effects on stabilization. With the help of noise stabilization, the stabilization of the other layers networks is realized based on the stability of the first layer networks and the characteristics of the superior coupling that is based on white noises. By employing graph theory and the Lyapunov method, an almost sure exponential stabilization criterion of the multi-layer networks is acquired. As a subsequent result, the proposed theory is applied to a class of stochastic coupled oscillators with sufficient conditions being given to ensure their stability. Finally, a numerical example is provided to illustrate the feasibility of the stated theoretical results.     

Chaos projective synchronization of the chaotic finance system with parameter switching perturbation and input time‐varying delay

This paper discusses some basic dynamical properties of the chaotic finance system with parameter switching perturbation, and investigates chaos projective synchronization of the chaotic finance system with the time‐varying delayed feedback controller, which are not fully considered in the existing research. Different from the previous methods, in this paper, the delayed feedback controller is not only time‐varying, but also the time‐varying delay is adaptive. Finally, an illustrate example is provided to show the effectiveness of this method. Copyright © 2014 John Wiley & Sons, Ltd.     

Pinning sampled‐data synchronization of complex dynamical networks with Markovian jumping and mixed delays using multiple integral approach

This study deals with the pinning synchronization problem for complex dynamical networks (CDNs) with Markovian jumping parameters and mixed delays under sampled‐data control technique. The mixed delays cover both discrete and distributed delays. The Markovian jumping parameters are modeled as a continuous‐time, finite‐state Markov chain. The sufficient conditions for asymptotic synchronization of considered networks are obtained by utilizing novel Lyapunov‐Krasovskii functional and multiple integral approach. The obtained criteria is formulated in terms of LMIs, which can be checked for feasibility by making use of available softwares. Lastly, numerical simulation results are presented to validate the advantage of the propound theoretical results. © 2016 Wiley Periodicals, Inc. Complexity 21: 622–632, 2016     

Synchronization of fractional‐order delayed neural networks with hybrid coupling

This article presents new theoretical results on the synchronization for a class of fractional‐order delayed neural networks with hybrid coupling that contains constant coupling and discrete‐delay coupling. This is the first attempt to investigate the synchronization problem of fractional‐order coupled delayed neural networks. Based on the fractional‐order Lyapunov stability theorem and Kronecker product properties, sufficient criteria are established to ensure the fractional‐order coupled neural network to achieve synchronization. Numerical simulations are given to illustrate the correctness of the theoretical results. © 2015 Wiley Periodicals, Inc. Complexity 21: 106–112, 2016     

Adaptive synchronization under almost every initial data for stochastic neural networks with time-varying delays and distributed delays

This paper is concerned with the adaptive synchronization problem for a class of stochastic delayed neural networks. Based on the LaSalle invariant principle of stochastic differential delay equations and the stochastic analysis theory as well as the adaptive feedback control technique, a linear matrix inequality approach is developed to derive some novel sufficient conditions achieving complete synchronization of unidirectionally coupled stochastic delayed neural networks. In particular, the synchronization criterion considered in this paper is the globally almost surely asymptotic stability of the error dynamical system, which has seldom been applied to investigate the synchronization problem. Moreover, the delays proposed in this paper are time-varying delays and distributed delays, which have rarely been used to study the synchronization problem for coupled stochastic delayed neural networks. Therefore, the results obtained in this paper are more general and useful than those given in the previous literature. Finally, two numerical examples and their simulations are provided to demonstrate the effectiveness of the theoretical results.     

Adaptive pinning synchronization of a class of nonlinearly coupled complex networks

This paper is concerned with the pinning control of the robust synchronization of a class of nonlinearly coupled complex networks through adaptive techniques. The effect of perturbed couplings is addressed by adaptive compensation and adjustment methods with controllers and coupling strength designs, respectively. For the pinned nodes, a controller gain function is proposed to compensate the nonlinearities based on adaptive estimations of controller parameters on-line; while for the un-pinned nodes, adaptive adjustment laws are addressed to adjust unknown coupling factors to restrain the unexpected action of the nonlinearly coupled networks. On the basis of Lyapunov stability theory, adaptive pinning controllers and coupling strength adjusters are constructed to ensure that the synchronization errors of the networks can be reduced as small as desired in the presence of the nonlinear couplings. A numerical simulation is provided to illustrate the effectiveness of the theoretical results.     

Synchronization of complex networks with time‐varying inner coupling and outer coupling matrices

Synchronization of complex networks with time‐varying coupling matrices is studied in this paper. Two kinds of time‐varying coupling are taken into account. One is the time‐varying inner coupling in the node state space and the other is the time‐varying outer coupling in the network topology space. By respectively setting linear controllers and adaptive controllers, time‐varying complex networks can be synchronized to a desired state. Meanwhile, different influences of the control parameters of linear controllers and adaptive controllers on the synchronization have also been investigated. Based on the Lyapunov function theory, we construct appropriate positive‐definite functions, and several sufficient synchronization criteria are obtained. Numerical simulations further illustrate the effectiveness of conclusions. Copyright © 2017 John Wiley & Sons, Ltd.     

Synchronization of memristor‐based delayed BAM neural networks with fractional‐order derivatives

This article deals with the problem of synchronization of fractional‐order memristor‐based BAM neural networks (FMBNNs) with time‐delay. We investigate the sufficient conditions for adaptive synchronization of FMBNNs with fractional‐order 0 < α < 1. The analysis is based on suitable Lyapunov functional, differential inclusions theory, and master‐slave synchronization setup. We extend the analysis to provide some useful criteria to ensure the finite‐time synchronization of FMBNNs with fractional‐order 1 < α < 2, using Mittag‐Leffler functions, Laplace transform, and linear feedback control techniques. Numerical simulations with two numerical examples are given to validate our theoretical results. Presence of time‐delay and fractional‐order in the model shows interesting dynamics. © 2016 Wiley Periodicals, Inc. Complexity 21: 412–426, 2016