Existence of almost periodic solution for SICNN with a neutral delay

Zheng Fang,Yongqing Yang

doi:10.14232/ejqtde.2011.1.30

Abstract

In this paper, a kind of shunting inhibitory cellular neural network with a neutral delay was considered. By using the Banach fixed point theorem, we established a result about the existence and uniqueness of the almost periodic solution for the shunting inhibitory cellular neural network.

Highlights

Shunting inhibitory cellular neural network (SICNN) is a kind of very important model and has been investigated by many authors due to its wide applications in practical fields such as robotics, adaptive pattern recognition and image processing
It is natural and useful to consider the model with a neutral delay, it means that the system describing the model depends on the past information of the state and the information of the derivative of the state, i.e., the decay rate of the cells
This kind of model is described by a differential equation with a neutral delay

Summary

Introduction

Shunting inhibitory cellular neural network (SICNN) is a kind of very important model and has been investigated by many authors (see [1, 2, 3, 4] and the reference therein) due to its wide applications in practical fields such as robotics, adaptive pattern recognition and image processing. 1e-mail: fangzhengjd@126.com, corresponding author 2e-mail: yyq640613@gmail.com shunting inhibitory cellular neural network with a neutral delay: x′ij = −aij(t)xij − Nr(i, j) = Ckl : max{| k − i |, | l − j |} ≤ r, 1 ≤ k ≤ m, 1 ≤ l ≤ n , xij(t) describes the state of the cell Cij, the coefficient aij(t) > 0 is the passive decay rate of the cell activity, Cikjl(t), Dikjl(t) are connection weights or coupling strength of postsynaptic activity of the cell Ckl transmitted to the cell Cij, and f, g are continuous activity functions, representing the output or firing rate of the cell Ckl , and τ (t), σ(t) correspond to the transmission delays.

Results

Conclusion