Synchronization in complex delayed dynamical networks with impulsive effects

The present paper is mainly concerned with the issues of synchronization dynamics of complex delayed dynamical networks with impulsive effects. A general model of complex delayed dynamical networks with impulsive effects is formulated, which can well describe practical architectures of more realistic complex networks related to impulsive effects. Based on impulsive stability theory on delayed dynamical systems, some simple but less conservative criterion are derived for global synchronization of such dynamical network. It is shown that synchronization of the networks is heavily dependent on impulsive effects of connecting configuration in the networks. Furthermore, the theoretical results are applied to a typical SF network composing of impulsive coupled chaotic delayed Hopfield neural network nodes, and are also illustrated by numerical simulations.     

Adaptive global synchronization of a general complex dynamical network with non-delayed and delayed coupling

This Letter investigates the global synchronization of a general complex dynamical network with non-delayed and delayed coupling. Based on Lasalle's invariance principle, adaptive global synchronization criteria is obtained. Analytical result shows that under the designed adaptive controllers, a general complex dynamical network with non-delayed and delayed coupling can globally asymptotically synchronize to a given trajectory. What is more, the node dynamic need not satisfy the very strong and conservative uniformly Lipschitz condition and the coupling matrix is not assumed to be symmetric or irreducible. Finally, numerical simulations are presented to verify the effectiveness of the proposed synchronization criteria.     

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.     

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.     

The impulsive control synchronization of the drive-response complex system

This Letter investigates projective synchronization between the drive system and response complex dynamical system. An impulsive control scheme is adapted to synchronize the drive-response dynamical system to a desired scalar factor. By using the stability theory of the impulsive differential equation, the criteria for the projective synchronization are derived. The feasibility of the impulsive control of the projective synchronization is demonstrated in the drive-response dynamical system.     

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.     

Global Synchronization of General Delayed Dynamical Networks

Global synchronization of general delayed dynamical networks with linear coupling are investigated. A sufficient condition for the global synchronization is obtained by using the linear matrix inequality and introducing a reference state. This condition is simply given based on the maximum nonzero eigenvalue of the network coupling matrix. Moreover, we show how to construct the coupling matrix to guarantee global synchronization of network, which is very convenient to use. A two-dimension system with delay as a dynamical node in network with global coupling is finally presented to verify the theoretical results of the proposed global synchronization scheme.     

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.     

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.     

Robust adaptive synchronization of dynamical networks via scalar controllers

Based on high gain feedback control theory, robust adaptive synchronization of dynamical network is investigated in this paper. When the non-linear coupling functions are unknown but with unknown bounded, some fairly simple robust adaptive scalar feedback controllers are derived. The key idea is that a time-varying gain parameter is introduced in designing controllers which can guarantee that the states of uncertain coupled dynamical networks robust adaptive asymptotically synchronize with each other. Numerical simulation is given to validate the proposed theoretical result.     

Projective Synchronization in Drive--Response Networks via Impulsive Control

Impulsive projective synchronization in 1 ＋N coupled chaotic systems are investigated with the drive-response dynamical network （DRDN） model. Based on impulsive stability theory, some simple but less conservative criteria axe achieved for projective synchronization in DRDNs. Furthermore, impulsive pinning scheme is also adopted to direct the scaring factor onto the desired value. Numerical simulations on generalized chaotic unified system axe illustrated to verify the theoretical results.     

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.     

Impulsive control of time-delay systems using delayed impulse and its application to impulsive master-slave synchronization

This Letter is concerned with impulsive control of a class of nonlinear time-delay systems. Some uniform stability criteria for the closed-loop time-delay system under delayed impulsive control are derived by using piecewise Lyapunov functions. Then the criteria are applied to impulsive master-slave synchronization of some secure communication systems with transmission delays and sample delays under delayed impulsive control. Two numerical examples are given to illustrate the effectiveness of the derived results.     

Impulsive synchronization of complex networks with non-delayed and delayed coupling

This Letter investigates the impulsive synchronization between two complex networks with non-delayed and delayed coupling. Based on the stability analysis of impulsive differential equation, the criteria for the synchronization is derived, and a linear impulsive controller and the simple updated laws are designed. Particularly, the weight configuration matrix is not necessarily symmetric or irreducible, and the inner coupling matrix need not be symmetric. Numerical examples are presented to verify the effectiveness and correctness of the 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.     

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.     

Synchronization of complex dynamical networks with nonidentical nodes

This Letter investigates the synchronization problem of a complex network with nonidentical nodes, and proposes two effective control schemes to synchronize the network onto any smooth goal dynamics. By applying open-loop control to all nodes and placing adaptive feedback injections on a small fraction of network nodes, a low-dimensional sufficient condition is derived to guarantee the global synchronization of the complex network with nonidentical nodes. By introducing impulsive effects to the open-loop controlled network, another synchronization scheme is developed for the network composed of nonidentical nodes, and an upper bound of impulsive intervals is estimated to ensure the global stability of the synchronization process. Numerical simulations are given to verify the theoretical 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.     

Robust impulsive synchronization of coupled delayed neural networks with uncertainties

This paper investigates the synchronization scheme of coupled neural networks with time delays. The coupling function, which can be linear or nonlinear, is subject to uncertainties in the network. By utilizing the stability theory for impulsive functional differential equations, several new criteria are obtained to ensure the robust synchronization of coupled networks via impulsive control. Furthermore, an estimation of the predicted stable region is derived to facilitate the design of the control gain. Finally, numerical simulations are presented to demonstrate the effectiveness of our results.     

Fixed-Time Synchronization Control of Delayed Dynamical Complex Networks

Fixed-time synchronization problem for delayed dynamical complex networks is explored in this paper. Compared with some correspondingly existed results, a few new results are obtained to guarantee fixed-time synchronization of delayed dynamical networks model. Moreover, by designing adaptive controller and discontinuous feedback controller, fixed-time synchronization can be realized through regulating the main control parameter. Additionally, a new theorem for fixed-time synchronization is used to reduce the conservatism of the existing work in terms of conditions and the estimate of synchronization time. In particular, we obtain some fixed-time synchronization criteria for a type of coupled delayed neural networks. Finally, the analysis and comparison of the proposed controllers are given to demonstrate the validness of the derived results from one numerical example.