Impulsive synchronization of two nonidentical chaotic systems with time-varying delay

This Letter investigates synchronization of two nonidentical Lur'e systems with time-varying delay and parameter mismatches via impulsive control. Based on the theory of impulsive functional differential equations, sufficient conditions for impulsive synchronization with a bound on the synchronization error are derived. An illustrative example is provided to validate the proposed method.     

Impulsive generalized function synchronization of complex dynamical networks

This Letter investigates generalized function synchronization of continuous and discrete complex networks by impulsive control. By constructing the reasonable corresponding impulsively controlled response networks, some criteria and corollaries are derived for the generalized function synchronization between the impulsively controlled complex networks, continuous and discrete networks are both included. Furthermore, the generalized linear synchronization and nonlinear synchronization are respectively illustrated by several examples. All the numerical simulations demonstrate the correctness of the theoretical results.     

Impulsive control and synchronization of a new chaotic system

This Letter derives some sufficient conditions for the stabilization and synchronization of the new chaotic system proposed by [G.Y. Qi, et al., Physica A 352 (2005) 295] via an impulsive method. Some new and less conservative criteria for the global exponential stability and asymptotical stability of impulsively controlled new chaotic system are obtained with varying impulsive intervals. In particular, some simple and easily verified criteria are established with equivalent impulsive intervals. An illustrative example is finally included to visualize the effectiveness and feasibility of the developed methods.     

Impulsive control of chaotic systems and its applications in synchronization

In this paper,some novel sufficient conditions for asymptotic stability of impulsive control systems are presented by comparison systems.The results are used to obtain the conditions under which the chaotic systems can be asymptotically controlled to the origin via impulsive control.Compared with some existing results,our results are more relaxed in the sense that the Lyapunov function is required to be nonincreasing only along a subsequence of switchings.Moreover,a larger upper bound of impulsive intervals for stabilization and synchronization is obtained.     

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.     

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.     

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.     

基于比较系统方法的分数阶混沌系统脉冲同步控制

针对一类分数阶混沌系统的同步问题, 提出基于比较系统理论的脉冲同步方法. 通过构造新的响应系统, 可将原分数阶同步误差系统转化为整数阶同步误差系统, 基于Lyapunov稳定性理论与脉冲微分方程理论, 给出一组新的分数阶混沌系统全局渐近同步判据. 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, 所得充分条件更为严格和实用. 通过对分数阶Chen系统同步问题的数值仿真研究, 验证了所提方法的有效性和可行性.     

模态分解法在非恒同耦合系统同步研究中的推广

通过改变耦合函数将模态分解法进行了推广,应用于非恒同耦合系统同步的研究.详细研究了周期吸引子、概周期吸引子等非恒同耦合系统的同步,得到了同步的局部渐近稳定性条件.并进行了数值模拟,发现同步时动力学现象丰富.概周期吸引子耦合系统会出现稳定的周期、概周期同步解,由于耦合周期吸引子耦合系统会出现多个稳定的周期同步解,且其吸引域差别较大,均出现了同步的多值性.同时也验证了该方法的正确性.     

Cluster synchronization in fractional-order complex dynamical networks

Cluster synchronization of complex dynamical networks with fractional-order dynamical nodes is discussed in the Letter. By using the stability theory of fractional-order differential system and linear pinning control, a sufficient condition for the stability of the synchronization behavior in complex networks with fractional order dynamics is derived. Only the nodes in one community which have direct connections to the nodes in other communities are needed to be controlled, resulting in reduced control cost. A numerical example is presented to demonstrate the validity and feasibility of the obtained result. Numerical simulations illustrate that cluster synchronization performance for fractional-order complex dynamical networks is influenced by inner-coupling matrix, control gain, coupling strength and topological structures of the networks.     

Adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems

In this paper, the adaptive impulsive synchronization for a class of fractional-order chaotic and hyperchaotic systems with unknown Lipschitz constant is investigated. Firstly, based on the adaptive control theory and the impulsive differential equations theory, the impulsive controller, the adaptive controller and the parametric update law are designed, respectively. Secondly, by constructing the suitable response system, the original fractional-order error system can be converted into the integral-order one. Finally, the new sufficient criterion is derived to guarantee the asymptotical stability of synchronization error system by the Lyapunov stability theory and the generalized Barbalat's lemma. In addition, numerical simulations demonstrate the effectiveness and feasibility of the proposed adaptive impulsive control method.     

Stochastic synchronization for time-varying complex dynamical networks

This paper studies the stochastic synchronization problem for time-varying complex dynamical networks. This model is totally different from some existing network models. Based on the Lyapunov stability theory, inequality techniques, and the properties of the Weiner process, some controllers and adaptive laws are designed to ensure achieving stochastic synchronization of a complex dynamical network model. A sufficient synchronization condition is given to ensure that the proposed network model is mean-square stable. Theoretical analysis and numerical simulation fully verify the main results.     

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.     

Adaptive pinning synchronization in fractional-order complex dynamical networks

Synchronization of general complex dynamical networks with fractional-order dynamical nodes is addressed in this paper. Based on the stability theory of fractional-order differential systems and adaptive pinning control, some sufficient local asymptotical synchronization criteria and global asymptotical ones are derived respectively, which succeed in solving the problem about how many nodes are need to be controlled and how much coupling strength should be applied to ensure the synchronization of the entire fractional-order networks. The obtained results are more general and effective than those reported. Moreover, the coupling-configuration matrices and the inner-coupling matrices are not assumed to be symmetric and irreducible. Finally, a numerical simulation is presented to demonstrate the validity and feasibility of the proposed synchronization criteria.     

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.     

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.     

Adaptive impulsive synchronization of uncertain chaotic systems

The Letter develops an adaptive impulsive scheme that includes a sole restriction criterion to achieve synchronization of chaotic nonlinear systems with unknown parameters. The system is assumed to satisfy the local Lipschitz condition while a Lipschitz constant and the uncertain system parameters are estimated by augmented adaptation equations. Adaptation of all parameters is proven to converge exponentially. The significance of the related control parameters and their margins in the criterion is also discussed in detail. The Lorenz system has been simulated to illustrate the theoretical analysis.     

Function projective synchronization in drive-response dynamical network

In this Letter, the function projective synchronization in the drive-response dynamical network is investigated, where the response dynamical network is affected not only by the drive system, but also coupled via a linearly feedback scheme. Based on Lyapunov stability theory, it is shown that the function projective synchronization with desired scaling function can be realized in the drive-response dynamical network by a simple control law. Moreover it is no need for the scaling function to be differentiable, bounded and nonzero all the time. The numerical simulations are provided to verify the theoretical result.