Periodic solutions for stochastic shunting inhibitory cellular neural networks with distributed delays

Li Yang,Yongkun Li

doi:10.1186/1687-1847-2014-37

Abstract

In this paper, by using an integral inequality, we establish some sufficient conditions ensuring the existence and p-exponential stability of periodic solutions for a class of stochastic shunting inhibitory cellular neural networks (SICNNs) with distributed delays. Moreover, we present an example to illustrate the feasibility of our theoretical results.

Highlights

The shunting inhibitory cellular neural networks (SICNNs) have been described as new cellular neural networks by Bouzerdout and Pinter in [ – ]
The layers in SICNNs are arranged into two-dimensional arrays of processing units called cells, where each cell is coupled to its neighboring units only
In [ – ], the authors considered the existence and stability of almost periodic solutions for SCINNs; in [, ], the authors considered the existence and stability of periodic solutions for SCINNs; in [ – ], the authors considered the existence and stability of antiperiodic solutions for impulsive SCINNs; in [, ], the authors obtained some sufficient conditions for the existence and stability of an equilibrium point

Summary

Introduction

The shunting inhibitory cellular neural networks (SICNNs) have been described as new cellular neural networks by Bouzerdout and Pinter in [ – ]. To the best of our knowledge, there is no paper published on the existence and stability of periodic solutions of stochastic shunting inhibitory cellular neural networks. Motivated by the above discussion, our main purpose of this paper is by using an integral inequality to obtain some sufficient conditions for the existence and p-exponential stability of periodic solutions in the case of the following stochastic shunting inhibitory cellular neural network with distributed delays: dxij(t) = –aij(t)xij(t) –. The main aim of this paper is to obtain some sufficient conditions on the existence and p-exponential stability of periodic solutions for ) is said to be p-exponentially stable, if there are constants λ > and M > such that for any solution y(t, t , φ ) with initial value φ ∈ BCFb ([–τ , ], Rn) of Suppose further that (H ) there exists an integer p > such that θ – θ min(i,j){aij}, lp (

Dkijl lij

Lij aij p

By and