Delay-dependent asymptotic stability for neural networks with time-varying delays

Xiaofeng Liao,Wei Zhang,Xiaofan Yang

doi:10.1155/ddns/2006/91725

Abstract

We study the dynamical behavior of a class of neural network models with time-varying delays. By constructing suitable Lyapunov functionals, we obtain sufficient delay-dependent criteria to ensure local and global asymptotic stability of the equilibrium of the neural network. Our results are applied to a two-neuron system with delayed connections between neurons, and some novel asymptotic stability criteria are also derived. The obtained conditions are shown to be less conservative and restrictive than those reported in the known literature. Some numerical examples are included to demonstrate our results.

Highlights

An artificial neural network model is usually described by a system of ordinary differential equations
Experimental studies have demonstrated that, in general, time delays exist in electronic circuits because of the finite switching speed of amplifiers and the model should be described by the system of delay differential equations
We note that, if the neural system starts with a stable equilibrium, but becomes unstable due to delays, it will likely be destabilized by means of a Hopf bifurcation leading to periodic solutions with small amplitudes [14, 15, 18]

Summary

Introduction

An artificial neural network model is usually described by a system of ordinary differential equations. Global asymptotic stability of the equilibrium of neural network with time delays, which is more important and usually more difficult to analyze than local stability, is investigated in [7,8,9,10,11,12,13, 16, 17, 19, 20, 22] by Lyapunov functions. We will give some new criteria for local and global asymptotic stability of the equilibrium of neural networks with time-varying delays. By Lemma 2.1, we see that for any sufficiently small positive constant ε, there exists a sufficiently large time, T = T(ε) > 0, such that for t ≥ T, ui(t) ≤ Ni + ε, i = 1, 2, .

Stability analysis

Application to two-neuron system with delays

Conclusions