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.     

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.     

Robust lag synchronization between two different chaotic systems via dual-stage impulsive control

In this paper, an improved impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the new definition of synchronization with error bound and a novel impulsive control scheme (the so-called dual-stage impulsive control), some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined level, which is more reasonable and rigorous than the existing results. In particular, some simpler and more convenient conditions are derived by taking the same impulsive distances and control gains. Finally, some numerical simulations for the Lorenz system and the Chen system are given to demonstrate the effectiveness and feasibility of the proposed method.     

Adaptive lag synchronization of uncertain dynamical systems with time delays via simple transmission lag feedback

In this paper we present an adaptive scheme to achieve lag synchronization for uncertain dynamical systems with time delays and unknown parameters. In contrast to the nonlinear feedback scheme reported in the previous literature, the proposed controller is a linear one which only involves simple feedback information from the drive system with signal popagation lags. Besides, the unknown parameters can also be identified via the proposed updating laws in spite of the existence of model delays and transmission lags, as long as the linear independence condition between the related function elements is satisfied. Two examples, i.e., the Mackey-Glass model with single delay and the Lorenz system with multiple delays, are employed to show the effectiveness of this approach. Some robustness issues are also discussed, which shows that the proposed scheme is quite robust in switching and noisy environment.     

Cluster projective synchronization of complex networks with nonidentical dynamical nodes

We investigate a new cluster projective synchronization(CPS) scheme in time-varying delay coupled complex dynamical networks with nonidentical nodes.Based on the community structure of the networks,the controllers are designed differently for the nodes in one community,which have direct connections to the nodes in the other communities and the nodes without direct connections to the nodes in the other communities.Some sufficient criteria are derived to ensure the nodes in the same group projectively synchronize and there is also projective synchronization between nodes in different groups.Particularly,the weight configuration matrix is not assumed to be symmetric or irreducible.The numerical simulations are performed to verify the effectiveness of the theoretical results.     

Structure identification of an uncertain network coupled with complex-variable chaotic systems via adaptive impulsive control

In this paper, structure identification of an uncertain network coupled with complex-variable chaotic systems is in- vestigated. Both the topological structure and the system parameters can be unknown and need to be identified. Based on impulsive stability theory and the Lyapunov function method, an impulsive control scheme combined with an adaptive strategy is adopted to design effective and universal network estimators. The restriction on the impulsive interval is relaxed by adopting an adaptive strategy. Further, the proposed method can monitor the online switching topology effectively. Several numerical simulations are provided to illustrate the effectiveness of the theoretical results.     

Impulsive synchronization of a nonlinear coupled complex network with a delay node

We investigate the impulsive synchronization of a nonlinear coupled complex network with a delay node.Both delay coupling and non-delay coupling,as well as the symmetrical coupling matrix and the asymmetrical coupling matrix are considered.Based on the comparison theorem of an impulsive differential system,some novel synchronization criteria are derived.Finally,numerical simulations demonstrate the effectiveness of the proposed synchronization criteria.     

Impulsive synchronization of a nonlinear coupled complex network with a delay node

We investigate the impulsive synchronization of a nonlinear coupled complex network with a delay node. Both delay coupling and non-delay coupling, as well as the symmetrical coupling matrix and the asymmetrical coupling matrix are considered. Based on the comparison theorem of an impulsive differential system, some novel synchronization criteria are derived. Finally, numerical simulations demonstrate the effectiveness of the proposed synchronization criteria.     

Cluster synchronization in a network of non-identical dynamic systems

Cluster synchronization in a network of non-identical dynamic systems is studied in this paper, using two-cluster synchronization for detailed analysis and discussion. The results show that the common intercluster coupling condition is not always needed for the diffusively coupled network. Several sufficient conditions are obtained by using the Schur unitary triangularization theorem, which extends previous results. Some numerical examples are presented for illustration.     

Complete synchronization of uncertain chaotic dynamical network via a simple adaptive control

In this paper, based on the invaxiance principle of differential equations, we propose a simple adaptive control method to synchronize the network with coupling of the general form. Comparing with other control approaches, this scheme only depends on each node＇s state output. So we need not to know the concrete network structure and the solutions of the isolate nodes of the network in advance. In order to demonstrate the effectiveness of the method, a special example is provided and numerical simulations are performed. The numerical results show that our control scheme is very effective and robust against the weak noise.     

Complete synchronization of uncertain chaotic dynamical network via a simple adaptive control

In this paper, based on the invariance principle of differential equations, we propose a simple adaptive control method to synchronize the network with coupling of the general form. Comparing with other control approaches, this scheme only depends on each node's state output. So we need not to know the concrete network structure and the solutions of the isolate nodes of the network in advance. In order to demonstrate the effectiveness of the method, a special example is provided and numerical simulations are performed. The numerical results show that our control scheme is very effective and robust against the weak noise.     

基于改进脉冲控制方法的超混沌系统同步

针对一类整数阶与分数阶超混沌系统的同步问题, 分别提出了改进的脉冲同步方法. 基于Lyapunov稳定性理论与脉冲微分方程理论, 给出超混沌系统一组新的全局渐近同步判据. 特别地, 当脉冲间距与脉冲控制增益为常数时, 可获得更为简单和实用的同步判据. 与现有结果相比, 所得充分条件更次保守且更为实用. 通过对超混沌Chen系统同步的数值仿真研究, 验证了所提方法的有效性和可行性.     

Impulsive control of nonlinear systems with time-varying delays

A whole impulsive control scheme of nonlinear systems with time-varying delays, which is an extension for impulsive control of nonlinear systems without time delay, is presented in this paper. Utilizing the Lyapunov functions and the impulsive-type comparison principles, we establish a series of different conditions under which impulsively controlled nonlinear systems with time-varying delays are asymptotically stable. Then we estimate upper bounds of impulse interval and time-varying delays for asymptotically stable control. Finally a numerical example is given to illustrate the effectiveness of the method.     

An improved impulsive control approach to robust lag synchronization between two different chaotic systems

In this paper, a novel robust impulsive lag synchronization scheme for different chaotic systems with parametric uncertainties is proposed. Based on the theory of impulsive functional differential equations and a new differential inequality, some new and less conservative sufficient conditions are established to guarantee that the error dynamics can converge to a predetermined region. Finally, some numerical simulations for the Lorenz system and Chen system are given to demonstrate the effectiveness and feasibility of the proposed method. Compared with the existing results based on so-called dual-stage impulsive control, the derived results reduce the complexity of impulsive controller, moreover, a larger stable region can be obtained under the same parameters, which can be shown in the numerical simulations finally.     

An improved impulsive control approach to nonlinear systems with time-varying delays

A scheme for the impulsive control of nonlinear systems with time-varying delays is investigated in this paper. Based on the Lyapunov-like stability theorem for impulsive functional differential equations (FDEs), some sufficient conditions are presented to guarantee the uniform asymptotic stability of impulsively controlled nonlinear systems with time-varying delays. These conditions are more effective and less conservative than those obtained. Finally, two numerical examples are provided to demonstrate the effectiveness of the proposed method.     

Modified impulsive synchronization of fractional order hyperchaotic systems

In this paper, a modified impulsive control scheme is proposed to realize the complete synchronization of fractional order hyperchaotic systems. By constructing a suitable response system, an integral order synchronization error system is obtained. Based on the theory of Lyapunov stability and the impulsive differential equations, some effective sufficient conditions are derived to guarantee the asymptotical stability of the synchronization error system. In particular, some simpler and more convenient conditions are derived by taking the fixed impulsive distances and control gains. Compared with the existing results, the main results in this paper are practical and rigorous. Simulation results show the effectiveness and the feasibility of the proposed impulsive control method.     

Exponential synchronization of complex delayed dynamical networks via pinning periodically intermittent control

The problem of synchronization for a class of complex delayed dynamical networks via pinning periodically intermittent control is considered in this Letter. Some novel and useful exponential synchronization criteria are obtained by utilizing the methods which are different from the techniques employed in the existing works, and the derived results are less conservative. Especially, the traditional assumptions on control width and time delays are released in our results. Moreover, a pinning scheme deciding what nodes should be chosen as pinned candidates and how many nodes are needed to be pinned for a fixed coupling strength is provided. A Barabási-Albert network example is finally given to illustrate the effectiveness of the theoretical results.     

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.     

Reliable impulsive synchronization for a class of nonlinear chaotic systems

The problem of reliable impulsive synchronization for a class of nonlinear chaotic systems has been investigated in this paper. Firstly a reliable impulsive controller is designed by using the impulsive control theory. Then by the uniform asymptotic stability criteria of systems with impulsive effects, some sufficient conditions for reliable impulsive synchronization between the drive system and the response system are obtained. Numerical simulations are given to show the effectiveness of the proposed method.     

Cluster synchronization in community network with nonidentical nodes via intermittent pinning control

In this paper, cluster synchronization in community network with nonidentical nodes is investigated. By combining intermittency with a pinning control scheme, some effective controllers are designed. In the control scheme, only one node in each community is controlled and coupling weights of a spanning tree in each community are enhanced. Based on the Lyapunov function method and mathematical analysis technique, two results for achieving cluster synchronization are obtained. Noticeably, by introducing an adaptive strategy, some universal adaptive intermittent pinning controllers are designed for different networks. Finally, two numerical simulations are performed to verify the correctness of the derived results.