Effects of heterogeneous impulses on synchronization of complex-valued neural networks with mixed time-varying delays

Abstract

This article investigates a new type of impulsive effect, namely the heterogeneous impulsive effect on the synchronization of complex-valued neural networks (CVNNs) with mixed time-varying delays. Heterogeneous impulsive effect is a unified framework of non-identical and time-varying impulses, i.e., the impulsive effect to state of each neuron is not only non-identical to each other but also distinct at different impulsive times. Here heterogeneous impulsive control is designed, which is an extension of hybrid impulsive control. The problem is studied with the following procedures. Firstly, the master–slave CVNNs are explicitly separated into two real-valued neural networks (RVNNs). Secondly, the two RVNNs are transformed into impulsive error dynamical system using the heterogeneous impulsive controller. Thirdly, the concepts of average impulsive interval (AII) and average impulsive gain (AIG) are implemented to obtain the synchronization of delayed CVNNs under heterogeneous impulsive effects. By employing a matrix measure method and extended impulsive Halanay inequality, sufficient criteria are derived to guarantee exponential synchronization of the given delayed CVNNs. The dependency of convergence rates on AIIs and AIGs is explicitly discussed. Finally, two examples are provided to show the efficiency of the proposed theoretical results.