Impacts of state-dependent impulses on the stability of switching Cohen-Grossberg neural networks

Xianxiu Zhang,Tingwen Huang,Chuandong Li

doi:10.1186/s13662-017-1375-z

Abstract

This paper investigates the impacts of state-dependent impulses on the stability of switching Cohen-Grossberg neural networks (CGNN) by means of B-equivalence method. Under certain conditions, the state-dependent impulsive switching systems can be reduced to the fixed-time ones. Furthermore, a stability criterion for the considered CGNN using the proposed comparison system is established. Finally, two numerical examples are provided to illustrate the efficiency of the theoretical results.

Highlights

The well-known Cohen-Grossberg neural networks (CGNN), which is a large class of artificial neural networks including the Hopfield neural network, the cellular neural network, the shunting neural networks, and some ecological systems, were initially proposed and studied by Cohen and Grossberg [ ] in
We study the global stability of switching CGNNs with state-dependent impulses, where the switches occur at the fixed time, while the impulses do not occur at fixed times
We obtain the quantitative relation between new jump operators and system state and show that the global stability of the corresponding comparison system implies the same stability of the considered state-dependent impulsive switching CGNN

Summary

Introduction

The well-known Cohen-Grossberg neural networks (CGNN), which is a large class of artificial neural networks including the Hopfield neural network, the cellular neural network, the shunting neural networks, and some ecological systems, were initially proposed and studied by Cohen and Grossberg [ ] in. We study the global stability of switching CGNNs with state-dependent impulses, where the switches occur at the fixed time, while the impulses do not occur at fixed times. We prove the existence of solution to switching CGNN with state-dependent impulse. We obtain the quantitative relation between new jump operators and system state and show that the global stability of the corresponding comparison system implies the same stability of the considered state-dependent impulsive switching CGNN. We consider the following switching Cohen-Grossberg neural networks with state-dependent impulses:. Definition ([ ]) The origin of system ( ) is said to be globally exponentially stable if there exist some constants γ > and M > such that x(t, t , x(t )) ≤ M exp(–γ (t – t )) for any t ≥ t

The conditions for absence of beating and B-equivalent method

Conclusions and discussions