Pinning Synchronization of Switched Complex Dynamical Networks

Synchronization of complex dynamical networks with switching topology: A switched system point of view

Adaptive synchronization of the complex dynamical network with non-derivative and derivative coupling

Finite-time synchronization of complex dynamical networks under delayed impulsive effects

Function projective synchronization in complex dynamical networks with time delay via hybrid feedback control

Although function projective synchronization in complex dynamical networks has been extensively studied in the literature, few papers deal with the problem between two different complex networks with correlated random disturbances. In this paper, we present some novel techniques to analyze the problem of synchronization. A probability approach is introduced to obtain an almost sure synchronization criterion. We also present some efficient approaches to analyze the problem of exponential synchronization. For the problem of synchronization in some complex networks, our approaches not only can replace the LaSalle-type theorem but also allow improvements of existing results in the literature. Finally, some numerical examples are provided to demonstrate the effectiveness of the proposed approaches.

This paper investigates the synchronisation of nonlinear coupled complex dynamical networks with different nonlinear nodes and different orders by using decentralised dynamical compensation controllers. We propose a dynamical network mathematical model with similar nonlinear nodes, whose dimensions are different. For this kind of network model, the decentralised dynamical compensation controllers are designed for the state synchronisation of the coupled nodes. In addition, the synchronisation manifold is defined as an invariant manifold, which is regarded as the generalised case of dynamical networks with the same nodes’ dynamics. Furthermore, some stability criteria for the synchronisation are derived by means of rigorous theoretical analysis. Finally, numerical examples are presented to verify the effectiveness of the obtained theoretical results.

Finite-time synchronization of complex dynamic networks with impulsive control and actuator saturation: An LMI approach

On designing decentralized impulsive controllers for synchronization of complex dynamical networks with nonidentical nodes and coupling delays

Global power synchronization of complex dynamical networks with proportional delay and impulsive effects

This article addresses the global synchronization of fractional dynamical networks with both delayed and non-delayed couplings under a switching topology, where the coupling configuration matrices need not be commutative. By utilizing a modified fractional Razumikhin technique, the common Lyapunov function method and graph theory, we present a convenient and effective approach to establish reliable algebraic criteria for global synchronization. Our method effectively overcomes the challenges associated with fractional calculus, time delays, and switching topologies. A key finding is that global synchronization can be achieved more rapidly by adding additional edges to the coupling configuration graphs. Additionally, an illustrative example is provided to demonstrate the effectiveness of our theoretical results.

Complex networks are everywhere.Synchronization is a very important nonlinear phenomenon which universally exists in nature.Over the last decade,many researchers have further investigated the synchronization of complex dynamical networks,including identical synchronzation,clustering synchronization,partial synchronization,and so on.The characterization of synchronous speed of complex dynamical networks in most known res(?)lts is asymptotic.That is,complex networks can realize synchronization only when the time t tends to infinity.However,there are few results reported on how long complex networks can reach synchronization.Based on two kinds of typical complex dynamical networks with nonlinear coupling,this paper will further explore the finite-time synchronization of complex dynamical networks.In detail,under some suitable conditions,it is proved that the above complex dynamical networks can realize accurate synchronization within finite- time.Moreover,a typical numerical simulation is then given to validate the effectiveness of the proposed criteria for finitetime synchronization.It should be especially pointed out that the finite-time synchronization sucessfully overcomes the difficulty of infinite synchronous time.The above results have some important practical meaning for the real-world engineering application.

In this paper, it is mainly concerned with the issue of mean square modified function projective synchronization of uncertain complex network with multi-links and stochastic perturbations. The uncertain terms are the unknown topological structure which exists inside the complex network and the external noise is imposed to the network. In order to achieve the mean square modified function projective synchronization of complex dynamical network, a strict feedback controller and novel adaptive control laws are designed based on Lyapunov stability theory, inequality techniques, and the properties of the Weiner process to obtain several novel synchronization criterion. Furthermore, the effectiveness of the proposed control scheme is validated by numerical simulations.

This paper addresses the problem of adaptive pinning synchronization of complex dynamical networks with nonlinear delayed intrinsic dynamics and time-varying delays. By introducing decentralized adaptive strategies to both the coupling strengths and the feedback gains, it is proved that the complex dynamical network can synchronize with the desired state for the bounded time-varying delays even when only one node is informed, without any global information of the underlying network. Finally, some numerical simulations are given to verify the main results and show the superiority of these self-designed adaptive strategies.

This paper concentrates on the cluster synchronization such that each community achieves linear-generalized synchronization in complex networks. Here two control schemes are introduced to realize cluster synchronization. One is to adjust the coupling strength of edges which connect different groups automatically, and to use the pinning control simultaneously. The other scheme is to adjust the coupling strength of edges in each group and to select only one node in each group to control. Finally, we present some simulations to demonstrate the correction of our conclusion.

This paper focuses on the problem of exponential synchronization of complex dynamical networks (CDNs) with time-varying coupling delay and sampled-data. An improved synchronization criterion is derived for the considered CDNs in terms of the free-weighting matrix method and input delay approach. The design method of the desired sampled-data controller is proposed. The derived result is numerically shown to be less conservative than existing one.