Robust impulsive synchronization of complex delayed dynamical networks

This Letter investigates robust impulsive synchronization of complex delayed dynamical networks with nonsymmetrical coupling from the view of dynamics and control. Based on impulsive control theory on delayed dynamical systems, some simple yet generic criteria for robust impulsive synchronization are established. It is shown that these criteria can provide a novel and effective control approach to synchronize an arbitrary given delayed dynamical network to a desired synchronization state. Comparing with existing results, the advantage of the control scheme is that synchronization state can be selected as a weighted average of all the states in the network for the purpose of practical control strategy. Finally, numerical simulations are given to demonstrate the effectiveness of the proposed control methodology.     

Synchronization of time varying delayed complex networks via impulsive control

In this paper, we investigate the problem of synchronization for the time varying delayed complex dynamical networks via impulsive control method, several sufficient synchronization conditions are given, and we consider the impulsive control matrices are time varying delayed matrices. Furthermore, we found impulsive control does not always play an active role in synchronization although impulsive control strategy is cheaper and simpler than other control strategy. Finally, numerical simulations are also given to demonstrate the effectiveness of the proposed schemes.     

Synchronization of impulsively coupled complex networks

We investigate the synchronization of complex networks,which are impulsively coupled only at discrete instants.Based on the comparison theory of impulsive differential systems,a distributed impulsive control scheme is proposed for complex dynamical networks to achieve synchronization.The proposed scheme not only takes into account the influence of all nodes to network synchronization,which depends on the weight of each node in the network,but also provides us with a flexible method to select the synchronized state of the network.In addition,it is unnecessary for the impulsive coupling matrix to be symmetrical.Finally,the proposed control scheme is applied to a chaotic Lorenz network and Chua’s circuit network.Numerical simulations are used to illustrate the validity of this control scheme.     

Robust adaptive synchronization of uncertain and delayed dynamical complex networks with faulty network

<正>This paper presents a new robust adaptive synchronization method for a class of uncertain dynamical complex networks with network failures and coupling time-varying delays.Adaptive schemes are proposed to adjust controller parameters for the faulty network compensations,as well as to estimate the upper and lower bounds of delayed state errors and perturbations to compensate the effects of delay and perturbation on-line without assuming symmetry or irreducibility of networks.It is shown that,through Lyapunov stability theory,distributed adaptive controllers constructed by the adaptive schemes are successful in ensuring the achievement of asymptotic synchronization of networks in the present of faulty and delayed networks,and perturbation inputs.A Chua's circuit network example is finally given to show the effectiveness of the proposed synchronization criteria.     

Synchronization in complex delayed dynamical networks with nonsymmetric coupling

A new general complex delayed dynamical network model with nonsymmetric coupling is introduced, and then we investigate its synchronization phenomena. Several synchronization criteria for delay-independent and delay-dependent synchronization are provided which generalize some previous results. The matrix Jordan canonical formalization method is used instead of the matrix diagonalization method, so in our synchronization criteria, the coupling configuration matrix of the network does not required to be diagonalizable and may have complex eigenvalues. Especially, we show clearly that the synchronizability of a delayed dynamical network is not always characterized by the second-largest eigenvalue even though all the eigenvalues of the coupling configuration matrix are real. Furthermore, the effects of time-delay on synchronizability of networks with unidirectional coupling are studied under some typical network structures. The results are illustrated by delayed networks in which each node is a two-dimensional limit cycle oscillator system consisting of a two-cell cellular neural network, numerical simulations show that these networks can realize synchronization with smaller time-delay, and will lose synchronization when the time-delay increase larger than a threshold.     

Adaptive-impulsive synchronization of uncertain complex dynamical networks

This Letter studies adaptive-impulsive synchronization of uncertain complex dynamical networks. Based on the stability analysis of impulsive system, several network synchronization criteria for local and global adaptive-impulsive synchronization are established. Numerical example is also given to illustrate the results.     

Global synchronization in general complex delayed dynamical networks and its applications

The main objective of the present paper is further to investigate global synchronization of a general model of complex delayed dynamical networks. Based on stability theory on delayed dynamical systems, some simple yet less conservative criteria for both delay-independent and delay-dependent global synchronization of the networks are derived analytically. It is shown that under some conditions, if the uncoupled dynamical node is stable itself, then the network can be globally synchronized for any coupling delays as long as the coupling strength is small enough. On the other hand, if each dynamical node of the network is chaotic, then global synchronization of the networks is heavily dependent on the effects of coupling delays in addition to the connection configuration. Furthermore, the results are applied to some typical small-world (SW) and scale-free (SF) complex networks composing of coupled dynamical nodes such as the cellular neural networks (CNNs) and the chaotic FHN neuron oscillators, and numerical simulations are given to verify and also visualize the theoretical results.     

Cluster synchronization of community network with distributed time delays via impulsive control

Cluster synchronization is an important dynamical behavior in community networks and deserves further investigations.A community network with distributed time delays is investigated in this paper.For achieving cluster synchronization,an impulsive control scheme is introduced to design proper controllers and an adaptive strategy is adopted to make the impulsive controllers unified for different networks.Through taking advantage of the linear matrix inequality technique and constructing Lyapunov functions,some synchronization criteria with respect to the impulsive gains,instants,and system parameters without adaptive strategy are obtained and generalized to the adaptive case.Finally,numerical examples are presented to demonstrate the effectiveness of the theoretical results.     

Impulsive synchronization of two coupled complex networks with time-delayed dynamical nodes

In this paper, we investigate the impulsive synchronization between two coupled complex networks with time-delayed dynamical nodes. Based on the Lyapunov stability, the linear feedback control and the impulsive control theories, the linear feedback and the impulsive controllers are designed separately. By using the generalized Barbalat's lemma, the global asymptotic impulsive synchronization of the drive—response complex networks is derived and some corresponding sufficient conditions are also obtained. Numerical examples are presented to verify the effectiveness and the correctness of the synchronization criteria.     

节点含时滞的不确定复杂网络的自适应同步研究

研究了节点带有时滞,网络结构已知或者完全未知时的不确定动态网络模型的同步问题.基于李雅普诺夫稳定性理论,并按照参数的已知和未知情况分别设计了复杂网络同步控制器和复杂网络同步自适应控制器,给出了网络同步的充分条件,保证了动态网络渐进同步于任意指定的网络中的单独节点的状态.最后,数值结果表明了方法的有效性. 关键词： 自适应同步 不确定复杂网络 Lyapunov稳定理论     

Impulsive Cluster Synchronization in Community Network with Nonidentical Nodes

In this paper,cluster synchronization in community network with nonidentical nodes and impulsive effects is investigated.Community networks with two kinds of topological structure are investigated.Positive weighted network is considered first and external pinning controllers are designed for achieving cluster synchronization.Cooperative and competitive network under some assumptions is investigated as well and can achieve cluster synchronization with only impulsive controllers.Based on the stability analysis of impulsive differential equation and the Lyapunov stability theory,several simple and useful synchronization criteria are derived.Finally,numerical simulations are provided to verify the effectiveness of the derived results.     

Synchronization of impulsively coupled complex systems with delay

This paper investigates the synchronization of complex systems with delay that are impulsively coupled at discrete instants only. Based on the comparison theorem of impulsive differential system, a distributed impulsive control scheme is proposed to achieve the synchronization for systems with delay. In the control strategy, the influence of all nodes to network synchronization relies on its weight. The proposed control scheme is applied to the chaotic delayed Hopfield neural networks and numerical simulations are presented to demonstrate the effectiveness of the proposed scheme.     

Pinning impulsive synchronization of stochastic delayed coupled networks

In this paper,the pinning synchronization problem of stochastic delayed complex network (SDCN) is investigated by using a novel hybrid pinning controller. The proposed hybrid pinning controller is composed of adaptive controller and impulsive controller,where the two controllers are both added to a fraction of nodes in the network. Using the Lyapunov stability theory and the novel hybrid pinning controller,some sufficient conditions are derived for the exponential synchronization of such dynamical networks in mean square. Two numerical simulation examples are provided to verify the effectiveness of the proposed approach. The simulation results show that the proposed control scheme has a fast convergence rate compared with the conventional adaptive pinning method.     

Synchronization in Complex Networks with Multiple Connections

In this paper a class of networks with multiple connections are discussed. The multiple connections include two different types of links between nodes in complex networks. For this new model, we give a simple generating procedure. Furthermore, we investigate dynamical synchronization behavior in a delayed two-layer network, giving corresponding theoretical analysis and numerical examples.     

基于自适应-脉冲控制方法实现时变耦合驱动-响应复杂网络的投影同步

最近,对时变延迟网络的脉冲稳定性的研究大量出现,但通过自适应-脉冲控制方法获得的时变延迟网络同步准则却很少.本文中,运用自适应-脉冲控制方法,设计自适应反馈控制器、自适应律和线性脉冲控制器,研究时变耦合部分线性系统驱动-响应复杂网络的投影同步.获得时变耦合网络的自适应-脉冲投影同步准则.并且不需要网络的耦合构造矩阵是不可约的.另外,运用数值模拟证实方案的有效性和可行性.     

Outer Synchronization of Complex Networks by Impulse

This paper investigates outer synchronization of complex networks, especially, outer complete synchronization and outer anti-synchronization between the driving network and the response network. Employing the impulsive control method which is uncontinuous, simple, efficient, low-cost and easy to implement in practical applications, we obtain some sufficient conditions of outer complete synchronization and outer anti-synchronization between two complex networks. Numerical simulations demonstrate the effectiveness of the proposed impulsive control scheme.     

Impulsive synchronization of networked nonlinear dynamical systems

In this Letter, we investigate the problem of impulsive synchronization of networked multi-agent systems, where each agent can be modeled as an identical nonlinear dynamical system. Firstly, an impulsive control protocol is designed for network with fixed topology based on the local information of agents. Then sufficient conditions are given to guarantee the synchronization of the networked nonlinear dynamical system by using algebraic graph theory and impulsive control theory. Furthermore, how to select the discrete instants and impulsive constants is discussed. The case that the topologies of the networks are switching is also considered. Numerical simulations show the effectiveness of our theoretical results.     

Exponential synchronization of complex networks with nonidentical time-delayed dynamical nodes

In this Letter, exponential synchronization of a complex network with nonidentical time-delayed dynamical nodes is considered. Two effective control schemes are proposed to drive the network to synchronize globally exponentially onto any smooth goal dynamics. By applying open-loop control to all nodes and adding some intermittent controllers to partial nodes, some simple criteria for exponential synchronization of such network are established. Meanwhile, a pinning scheme deciding which nodes need to be pinned and a simply approximate formula for estimating the least number of pinned nodes are also provided. By introducing impulsive effects to the open-loop controlled network, another synchronization scheme is developed for the network with nonidentical time-delayed dynamical nodes, and an estimate of the upper bound of impulsive intervals ensuring global exponential stability of the synchronization process is also given. Numerical simulations are presented finally to demonstrate the effectiveness of the theoretical results.     

多重边融合复杂动态网络的自适应同步

基于网络拆分的思想对多重边融合复杂动态网络局部和全局的自适应同步进行了研究.通过给出严格的数学定义及假设,运用Lyapunov稳定理论得出了网络局部和全局的同步准则,给出了更为简单的网络同步的控制器.最后以Lorenz 系统为例进行数值仿真,验证了结论的正确性和有效性. 关键词： 多重边融合复杂动态网络 自适应同步 网络拆分 时滞     

Adaptive Impulsive Outer Synchronization Between Drive-Response Dynamical Networks

In this paper, outer synchronization between drive-response dynamical networks is investigated. Impulsive control combining with adaptive strategy is adopted to design controllers for achieving the goal. Based on the Lyapunov function method and mathematical analysis technique, a synchronization criterion with respect to the impulsive gains and intervals is analytically derived. From the criterion, the impulsive gains can adjust themselves to proper values when the impulsive intervals and some constants are fixed, and vice versa. Finally, two numerical examples are provided to verify the effectiveness of the derived result.