Adaptive Pinning Synchronization of Delayed Complex Dynamical Networks

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 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.

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

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

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

This paper proposes a general complex dynamical network model with two types of time-varying delays. The model is more general than those in the existing literatures in that it contains nonlinear coupling term which implies that the network topology can be known or unknown. Besides, the two types of delays consist of the system delay at each node and the coupling delay between nodes. Based on the Lyapunov stability theory, an adaptive synchronization criterion is proposed theoretically. An illustrated example is given to show the effectiveness of the theoretical result.

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

In this paper, in the case of quantized communication and coupling delays, a novel quantized pinning control (QPC) law is designed to deal with the synchronization problem of complex dynamic networks (CDN). Utilizing the Lyapunov method, non-smooth analysis tools and convex combination techniques, some sufficient criteria for achieving synchronization of CDNs with coupling delays are given. Finally, the effectiveness of the main results is demonstrated by presenting a simulation example.

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

The adaptive pinning synchronization control is presented, where the feedback control gain is based on the node energy index and the uncertainty is assumed to be unknown. For the sake of eliminating the uncertainty for the network synchronization, the adaptive pinning control is designed to compensate the uncertainties for the pinned nodes. Based on the BA scale-free networks, a simple numerical example is given to verify the effectiveness of the proposed method.

Adaptive projective lag synchronization of uncertain complex dynamical networks with disturbance

Network topology and node dynamics play a key role in forming synchronization of complex networks. Unfortunately there is no effective synchronization criterion for pinning synchronization of complex dynamical networks with switching topology. In this paper, pinning synchronization of complex dynamical networks with switching topology is studied. Two basic problems are considered: one is pinning synchronization of switched complex networks under arbitrary switching; the other is pinning synchronization of switched complex networks by design of switching when synchronization cannot achieved by using any individual connection topology alone. For the two problems, common Lyapunov function method and single Lyapunov function method are used respectively, some global synchronization criteria are proposed and the designed switching law is given. Finally, simulation results verify the validity of the results.

This paper deals with the synchronization problem of complex dynamical networks with interval time-varying coupling delays. A simple local linear feedback controller is introduced to guarantee the synchronizability of the networks. Some delay-dependent synchronization conditions for the controlled complex dynamical networks are presented by using the Lyapunov–Krasovskii functional method and the reciprocally convex combination approach. Theoretical analysis and numerical examples show that the obtained conditions have less computational complexity and less conservatism than some recently reported ones.

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.

This paper studies the synchronization of complex dynamical networks with multilinks and similar nodes. The dynamics of all the nodes in the networks are impossible to be completely identical due to the differences of parameters or the existence of perturbations. Networks with similar nodes are universal in the real world. In order to depict the similarity of the similar nodes, we give the definition of the minimal similarity of the nodes in the network for the first time. We find the threshold of the minimal similarity of the nodes in the network. If the minimal similarity of the nodes is bigger than the threshold, then the similar nodes can achieve synchronization without controllers. Otherwise, adaptive synchronization method is adopted to synchronize similar nodes in the network. Some new synchronization criteria are proposed based on the Lyapunov stability theory. Finally, numerical simulations are given to illustrate the feasibility and the effectiveness of the proposed theoretical results.