时变时滞耦合两个不同复杂网络的自适应广义同步

针对具有时变时滞耦合的两个不同复杂网络, 研究其广义同步问题. 基于Barbalat引理, 设计非线性自适应控制器使得两个网络获得广义同步. 进一步研究了具有未知拓扑结构的两个网络的广义同步问题. 数值仿真表明了本文方法的有效性.     

Exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and mode-dependent probabilistic time-varying delays

In this paper, the problem of exponential synchronization of complex dynamical networks with Markovian jumping parameters using sampled-data and Mode-dependent probabilistic time-varying coupling delays is investigated. The sam- pling period is assumed to be time-varying and bounded. The information of probability distribution of the time-varying delay is considered and transformed into parameter matrices of the transferred complex dynamical network model. Based on the condition, the design method of the desired sampled data controller is proposed. By constructing a new Lyapunov functional with triple integral terms, delay-distribution-dependent exponential synchronization criteria are derived in the form of linear matrix inequalities. Finally, two numerical examples are given to illustrate the effectiveness of the proposed methods.     

Novel criteria for exponential synchronization of inner time-varying complex networks with coupling delay

This paper mainly investigates the exponential synchronization of an inner time-varying complex network with coupling delay. Firstly, the synchronization of complex networks is decoupled into the stability of the corresponding dynamical systems. Based on the Lyapunov function theory, some sufficient conditions to guarantee its stability with any given convergence rate are derived, thus the synchronization of the networks is achieved. Finally, the results are illustrated by a simple time-varying network model with a coupling delay. All involved numerical simulations verify the correctness of the theoretical analysis.     

Exponential synchronization of chaotic Lur’e systems with time-varying delay via sampled-data control

In this paper, we study the exponential synchronization of chaotic Lur＇e systems with time-varying delays via sampled-data control by using sector nonlinearties. In order to make full use of information about sampling intervals and interval time-varying delays, new Lyapunov-Krasovskii functionals with triple integral terms are introduced. Based on the convex combination technique, two kinds of synchronization criteria are derived in terms of linear matrix inequal- ities, which can be efficiently solved via standard numerical software. Finally, three numerical examples are provided to demonstrate the less conservatism and effectiveness of the proposed 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.     

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.     

结点含时滞的具有零和非零时滞耦合的复杂网络混沌同步

时滞耦合的复杂网络同步已经有大量的研究成果,而网络结点含时滞的无时滞耦合的复杂网络同步的研究工作较少.为使网络模型更接近现实和适用更广的范围,建立了网络结点含时滞,而耦合兼零时滞(无时滞)和非零时滞(有时滞)的复杂网络同步模型.在网络结点上分别设置线性控制器和自适应控制器,研究了其混沌同步问题.利用李雅普诺夫稳定性定理,设计相应的正定函数,分别给出了复杂网络同步的充分条件.最后,为证实同步方案的有效性,选择时滞Logistic函数为结点动力系统,在兼无时滞和有时滞的网络上,给出了线性反馈控制同步误差数值演化趋势.     

Cluster exponential synchronization of a class of complex networks with hybrid coupling and time-varying delay

This paper deals with the cluster exponential synchronization of a class ot complex networks wlm nyorm coupm~g and time-varying delay. Through constructing an appropriate Lyapunov-Krasovskii functional and applying the theory of the Kronecker product of matrices and the linear matrix inequality （LMI） technique, several novel sufficient conditions for cluster exponential synchronization are obtained. These cluster exponential synchronization conditions adopt the bounds of both time delay and its derivative, which are less conservative. Finally, the numerical simulations are performed to show the effectiveness of the theoretical results.     

Impulsive effect on exponential synchronization of neural networks with leakage delay under sampled-data feedback control

We consider the impulsive effect on the exponential synchronization of neural networks with leakage delay under the sampled-data feedback control. We use an appropriate Lyapunov–Krasovskii functional combined with the input delay approach and some inequality techniques to derive sufficient conditions that ensure the exponential synchronization of the delayed neural network. The conditions are formulated in terms of the leakage delay, the sampling period, and the exponential convergence rate. Numerical examples are given to demonstrate the usefulness and the effectiveness of the results.     

Combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and disturbances

In this paper, the problem of combination projection synchronization of fractional-order complex dynamic networks with time-varying delay couplings and external interferences is studied. Firstly, the definition of combination projection synchronization of fractional-order complex dynamic networks is given, and the synchronization problem of the drive-response systems is transformed into the stability problem of the error system. In addition, time-varying delays and disturbances are taken into consideration to make the network synchronization more practical and universal. Then, based on Lyapunov stability theory and fractional inequality theory, the adaptive controller is formulated to make the drive and response systems synchronization by the scaling factors. The controller is easier to realize because there is no time-delay term in the controller. At last, the corresponding simulation examples demonstrate the effectiveness of the proposed scheme.     

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.     

New synchronization analysis for complex networks with variable delays

This paper deals with the issue of synchronization of delayed complex networks. Differing from previous results,the delay interval [0,d(t)] is divided into some variable subintervals by employing a new method of weighting delays. Thus,new synchronization criteria for complex networks with time-varying delays are derived by applying this weighting-delay method and introducing some free weighting matrices. The obtained results have proved to be less conservative than previous results. The sufficient conditions of asymptotical synchronization are derived in the form of linear matrix inequality,which are easy to verify. Finally,several simulation examples are provided to show the effectiveness of the proposed results.     

Pinning synchronization of time-varying delay coupled complex networks with time-varying delayed dynamical nodes

This paper deals with the pinning synchronization of nonlinearly coupled complex networks with time-varying coupling delays and time-varying delays in the dynamical nodes.We control a part of the nodes of the complex networks by using adaptive feedback controllers and adjusting the time-varying coupling strengths.Based on the Lyapunov-Krasovskii stability theory for functional differential equations and a linear matrix inequality(LMI),some sufficient conditions for the synchronization are derived.A numerical simulation example is also provided to verify the correctness and the effectiveness of the proposed scheme.     

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.     

Free-matrix-based time-dependent discontinuous Lyapunov functional for synchronization of delayed neural networks with sampled-data control

This paper is concerned with the synchronization of delayed neural networks via sampled-data control. A new technique, namely, the free-matrix-based time-dependent discontinuous Lyapunov functional approach, is adopted in constructing the Lyapunov functional, which takes advantage of the sampling characteristic of sawtooth input delay. Based on this discontinuous Lyapunov functional, some less conservative synchronization criteria are established to ensure that the slave system is synchronous with the master system. The desired sampled-data controller can be obtained through the use of the linear matrix inequality(LMI) technique. Finally, two numerical examples are provided to demonstrate the effectiveness and the improvements of the proposed methods.     

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.     

Successive lag synchronization on dynamical networks with communication delay

In this paper, successive lag synchronization(SLS) on a dynamical network with communication delay is investigated.In order to achieve SLS on the dynamical network with communication delay, we design linear feedback control and adaptive control, respectively. By using the Lyapunov function method, we obtain some sufficient conditions for global stability of SLS. To verify these results, some numerical examples are further presented. This work may find potential applications in consensus of multi-agent systems.     

Pinning control of weighted general complex dynamical networks with time delay

Time delays commonly exist in the real world. In the present work we consider weighted general complex dynamical networks with time delay, which are undirected and connected. Control of such networks, by applying local feedback injections to a fraction of network nodes, is investigated for both continuous-time and discrete-time cases. Both delay-independent and delay-dependent asymptotical stability criteria for network stabilization are derived. It is also shown that the whole network can be stabilized by controlling only one node. The efficiency of the derived results was illustrated by numerical examples.     

Generalized projective synchronization between two different general complex dynamical networks with delayed coupling

In this Letter, generalized projective synchronization (GPS) between two different complex dynamical networks with delayed coupling is investigated. Two complex networks are distinct if they have diverse node dynamics, or different number of nodes, or different topological structures. By using the adaptive control scheme, a sufficient synchronization criterion for this GPS is derived based on the LaSalle invariance principle. Three corollaries are also obtained. It is noticed that the synchronization speed sensitively depends on the adjustable positive constants μi. Furthermore, the coupling configuration matrix is not necessary to be symmetric or irreducible, and the inner coupling matrix need not be symmetric. In addition, the node dynamic need not satisfy the very strong and conservative uniformly Lipschitz condition. Numerical simulations further demonstrate the feasibility and effectiveness of the theoretical results.