Exponential synchronization of stochastic delayed discrete-time complex networks

This paper is concerned with the problem of synchronization for stochastic discrete-time drive-response networks with time-varying delay. By employing the Lyapunov functional method combined with the stochastic analysis as well as the feedback control technique, several sufficient conditions are established that guarantee the exponentially mean-square synchronization of two identical delayed networks with stochastic disturbances. These sufficient conditions, which are expressed in terms of linear matrix inequalities (LMIs), can be solved efficiently by the LMI toolbox in Matlab. A particular feature of the LMI-based synchronization criteria is that they are dependent not only on the connection matrices in the drive networks and the feedback gains in the response networks, but also on the lower and upper bounds of the time-varying delay, and are therefore less conservative than the delay-independent ones. Two numerical examples are exploited to demonstrate the feasibility and applicability of the proposed synchronization approaches.     

Adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling

This paper investigates the adaptive-impulsive projective synchronization of drive-response delayed complex dynamical networks with time-varying coupling, in which the weights of links between two connected nodes are time varying. By the stability analysis of the impulsive functional differential equation, the sufficient conditions for achieving projective synchronization are obtained, and a hybrid controller, that is, an adaptive feedback controller with impulsive control effects is designed. The numerical examples are presented to illustrate the effectiveness and advantage of the proposed synchronization criteria.     

Adaptive exponential synchronization in pth moment for stochastic time varying multi-delayed complex networks

In this paper, the analysis problem of adaptive exponential synchronization in pth moment is considered for stochastic complex networks with time varying multi-delayed coupling. By using the Lyapunov–Krasovskii functional, stochastic analysis theory, several sufficient conditions to ensure the mode adaptive exponential synchronization in pth moment for stochastic delayed complex networks are derived. To illustrate the effectiveness of the synchronization conditions derived in this paper, a numerical example is finally provided.     

Pinning cluster synchronization of delayed complex dynamical networks with nonidentical nodes and impulsive effects

Nonlinear Dynamics - This paper studies the exponential cluster synchronization problem of complex dynamical networks with delayed couplings and nonidentical nodes. A new type of pinning impulsive...     

Delayed impulsive synchronization of nonlinearly coupled Markovian jumping complex dynamical networks with stochastic perturbations

Nonlinear Dynamics - This paper focuses on the exponential synchronization of nonlinearly coupled Markovian jumping complex dynamical networks with stochastic perturbations under delayed impulsive...     

Composite synchronization control for delayed coupling complex dynamical networks via a disturbance observer-based method

Nonlinear Dynamics - Based on state feedback control approach and disturbance observer method, a new composite synchronization control strategy is presented in this study for a class of delayed...     

Adaptive synchronization of uncertain dynamical networks with delayed coupling

We propose a simple scheme for the synchronization of an uncertain complex dynamical network with delayed coupling. Based on the Lyapunov stability theory of functional differential equations, certain controllers can be designed for ensuring the states of uncertain dynamical network with coupling delays to globally asymptotically synchronize by combining the adaptive method and linear feedback with the updated feedback strength. Different update gains η _i will lead to different rates toward synchrony, the choice of which depends on the concrete systems and network models. This strategy can be applied to any complex dynamical network (regular, small-world, scale-free or random). Numerical examples with respectively nearest-neighbor coupling and scale-free structure are given to demonstrate the effectiveness of our presented scheme.     

Finite-time stochastic synchronization of time-delay neural networks with noise disturbance

Nonlinear Dynamics - The finite-time stochastic synchronization of time-delay neural networks with noise disturbance is investigated according to finite-time stability theory of stochastic...     

Almost sure cluster synchronization of Markovian switching complex networks with stochastic noise via decentralized adaptive pinning control

This paper investigates the issue of almost sure cluster synchronization in nonlinearly coupled complex networks with nonidentical nodes and time-varying delay. These networks are modulated by a continuous-time Markov chain and disturbed by a Brownian movement. The decentralized adaptive update law and pinning control protocol are employed in designing controllers for guaranteeing almost sure cluster synchronization. By constructing a novel stochastic Lyapunov–Krasovskii function and using the stochastic Lasalle-type invariance theorem, some sufficient conditions for almost sure cluster synchronization of the networks are derived. Finally, a numerical example is given to testify the effectiveness of the theoretical results.     

GLOBAL ASYMPTOTIC STABILITY CONDITIONS OF DELAYED NEURAL NETWORKS

1　IntroductionandProblemEductionRecently,thestudiesofthestabilityforcellularneuralnetworks (CNNs)anddelayedcellularneuralnetworks (DCNNs)haveattractedattentionsofresearchersandseveralimportantresultshavebeenobtained .MostpapersdealtwithcompletelystableCNNsandDCNNsthataresuitableforimageprocessingapplications.CNNshavebeenwidelyappliedtoimageprocessing ,toprocessmovingimages,onemustintroducedelaysinthesignalstransmittedamongthecells.Buttimedelaysmayleadtoanoscillationphenomenonand ,furt…     

Sampled-data-based lag synchronization of chaotic delayed neural networks with impulsive control

Nonlinear Dynamics - In the framework of sampled-data control, this paper deals with the lag synchronization of chaotic neural networks with time delay meanwhile taking the impulsive control into...     

Outer synchronization of complex networks with delay via impulse

Synchronization between the driving network and the responding network (outer synchronization) has attracted increasing attention from various fields of science and engineering. In this paper, we address outer synchronization of complex networks with delays. Both the cases of coupling delay and node delay are considered. Employing the impulsive control method which is simple, efficient, low cost, and easy to implement in practical applications, we obtain some sufficient conditions of outer synchronization. It indicates that outer synchronization can be achieved if the maximal impulsive intervals are less than a critical value. Numerical simulations are also given to demonstrate the effectiveness of the proposed impulsive control scheme.     

Finite-time synchronization of complex networks with nonidentical discontinuous nodes

In this paper, we study the finite-time synchronization problem for linearly coupled complex networks with discontinuous nonidentical nodes. Firstly, new conditions for general discontinuous chaotic systems is proposed, which is easy to be verified. Secondly, a set of new controllers are designed such that the considered model can be finite-timely synchronized onto any target node with discontinuous functions. Based on a finite-time stability theorem for equations with discontinuous right-hand and inequality techniques, several sufficient conditions are obtained to ensure the synchronization goal. Results of this paper are general, and they extend and improve existing results on both continuous and discontinuous complex networks. Finally, numerical example, in which a BA scale-free network with discontinuous Sprott and Chua circuits is finite-timely synchronized onto discontinuous Chen system, is given to show the effectiveness of our new results.     

Global synchronization in fixed time for semi-Markovian switching complex dynamical networks with hybrid couplings and time-varying delays

This paper is concerned with the global synchronization in fixed time for semi-Markovian switching complex dynamical networks with hybrid couplings and time-varying delays in the presence of disturbances. Firstly, the property with respect to the global stability in fixed time is developed for semi-Markovian switching nonlinear systems. Subsequently, a novel sliding manifold with double integration is presented based on the proposed principle of convergence in fixed time. Under the designed sliding mode controller, the state trajectory of synchronization error system is driven to the prescribed sliding manifold in fixed time. In addition, the global stability in fixed time of sliding mode dynamics is proved analytically. By means of the stochastic Lyapunov–Krasovskii functional approach, the synchronization condition is established in terms of linear matrix inequalities; moreover, the stochastic fixed settling-time can be determined to any desired values in advance, via the configuration of parameters in the proposed controller. Finally, two numerical examples are provided to demonstrate the validity of the theoretical results and the feasibility of the proposed approach.