Existence and p-exponential stability of periodic solution for stochastic shunting inhibitory cellular neural networks with time-varying delays

Yicheng Pang,Changjin Xu,Maoxin Liao

doi:10.1080/18756891.2016.1237192

Abstract

AbstractIn this paper, we investigate a class of stochastic shunting inhibitory cellular neural networks with time-varying delays. Applying integral inequality, some sufficient conditions on the existence and p-exponential stability of periodic solutions for stochastic shunting inhibitory cellular neural networks with time-varying delays are established. An example is presented to illustrate our main theoretical findings. Our results are new and complementary to previously known studies.

Highlights

Since shunting inhibitory cellular neural networks have been successfully applied to pattern recognition, image and signal processing, vision, and optimization, their dynamics has attracted many attentions
Gao et al.1 studied the existence and stability almost periodic solutions for cellular neural networks with time-varying delays in leakage terms on time scales, Liu and Shao2 analyzed the almost periodic solutions for SICNNs with time-varying delays in the leakage terms, Liu3 focused on the pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays, Armmaret al. 4 made a detailed discussion on the existence and uniqueness of pseudo almost periodic solutions of recurrent neural networks with time-varying coef
Xu et al / Existence and p-exponential stability ficients and mixed delays, Abbas and Xia 5 investigated the almost automorphic solutions of impulsive cellular neural networks with piecewise constant argument, Li and Shu 6 dealt with the antiperiodic solutions to impulsive shunting inhibitory cellular neural networks with distributed delays on time scales

Summary

Introduction

Since shunting inhibitory cellular neural networks have been successfully applied to pattern recognition, image and signal processing, vision, and optimization, their dynamics has attracted many attentions. Gao et al. studied the existence and stability almost periodic solutions for cellular neural networks with time-varying delays in leakage terms on time scales, Liu and Shao analyzed the almost periodic solutions for SICNNs with time-varying delays in the leakage terms, Liu focused on the pseudo almost periodic solutions for neutral type CNNs with continuously distributed leakage delays, Armmaret al. 4 made a detailed discussion on the existence and uniqueness of pseudo almost periodic solutions of recurrent neural networks with time-varying coef-. We will consider the following stochastic shunting inhibitory cellular neural networks with timevarying delays dxi j(t) = − ai j(t)xi j(t) + Li j(t).

Preliminaries

Existence of Periodic Solution

An Example with Its Numerical Simulations

Conclusions