Pinning-controlled synchronization of delayed neural networks with distributed-delay coupling via impulsive control

This paper proposes a directed complex dynamical network consisting of ${N}$ linearly and diffusively coupled identical reaction-diffusion neural networks. Based on the Lyapunov functional method and the pinning control technique, some sufficient conditions are obtained to guarantee the synchronization of the proposed network model. In addition, an adaptive strategy is proposed to obtain appropriate coupling strength for achieving network synchronization. Furthermore, the pinning adaptive synchronization problem is also investigated in this paper, and a general criterion for ensuring network synchronization is established. Finally, a numerical example is provided to illustrate the effectiveness of the proposed criteria.

Pinning Control for Synchronization of Coupled Reaction-Diffusion Neural Networks With Directed Topologies

This paper considers existence, uniqueness and the global asymptotic stability of fuzzy cellular neural networks with mixed delays. The mixed delays include constant delay in the leakage term (i.e., “leakage delay”), time-varying delays and continuously distributed delays. Based on the Lyapunov method and the linear matrix inequality (LMI) approach, some sufficient conditions ensuring global asymptotic stability of the equilibrium point are derived, which are dependent on both the discrete and distributed time delays. These conditions are expressed in terms of LMI and can be easily checked by MATLAB LMI toolbox. In addition, two numerical examples are given to illustrate the feasibility of the result.

Existence and global stability analysis of equilibrium of fuzzy cellular neural networks with time delay in the leakage term under impulsive perturbations

In this paper, we propose a general array model of coupled reaction-diffusion neural networks with hybrid coupling, which is composed of spatial diffusion coupling and state coupling. By utilizing the Lyapunov functional method combined with the inequality techniques, a sufficient condition is given to ensure that the proposed network model is synchronized. In addition, when the external disturbances appear in the network, a criterion is obtained to guarantee the H
 ∞
 synchronization of the network. Moreover, some adaptive strategies to tune the coupling strengths among network nodes are designed for reaching synchronization and H
 ∞
 synchronization. Some criteria for synchronization and H
 ∞
 synchronization are derived by using the designed adaptive laws. Numerical simulations are presented finally to demonstrate the effectiveness of the obtained theoretical results.

Synchronization and adaptive control of an array of linearly coupled reaction-diffusion neural networks with hybrid coupling.

This paper investigates exponential synchronization of coupled networks with hybrid coupling, which is composed of constant coupling and discrete-delay coupling. There is only one transmittal delay in the delayed coupling. The fact is that in the signal transmission process, the time delay affects only the variable that is being transmitted from one system to another, then it makes sense to assume that there is only one single delay contributing to the dynamics. Some sufficient conditions for synchronization are derived based on Lyapunov functional and linear matrix inequality (LMI). In particular, the coupling matrix may be asymmetric or nondiagonal. Moreover, the transmittal delay can be different from the one in the isolated system. A distinctive feature of this work is that the synchronized state will vary in comparison with the conventional synchronized solution. Especially, the degree of the nodes and the inner delayed coupling matrix heavily influence the synchronized state. Finally, a chaotic neural network is used as the node in two regular networks to show the effectiveness of the proposed criteria.

Kun Yuan

Papers

Exponential stability and periodic solutions of fuzzy cellular neural networks with time-varying delays

Robust synchronization in arrays of coupled networks with delay and mixed coupling

Cooperative tracking for nonlinear multi-agent systems with hybrid time-delayed protocol