Almost periodic solutions for neutral delay Hopfield neural networks with time-varying delays in the leakage term on time scales

Ling Li,Li Yang,Yongkun Li

doi:10.1186/1687-1847-2014-178

Abstract

In this paper, a class of neutral delay Hopfield neural networks with time-varying delays in the leakage term on time scales is considered. By utilizing the exponential dichotomy of linear dynamic equations on time scales, Banach’s fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solutions for this class of neural networks. Finally, a numerical example illustrates the feasibility of our results and also shows that the continuous-time neural network and the discrete-time analogue have the same dynamical behaviors. The results of this paper are completely new and complementary to the previously known results even when the time scale .

Highlights

The dynamical properties for delayed Hopfield neural networks have been extensively studied since they can be applied into pattern recognition, image processing, speed detection of moving objects, optimization problems and many other fields
To the best of our knowledge, up to now, there have been no papers published on the existence and stability of almost periodic solutions to neutral-type delay neural networks with time-varying delays in the leakage term on time scales
It is important and, in effect, necessary to study the existence of almost periodic solutions for neutral-type neural networks with time-varying delay in the leakage term on time scales

Summary

Introduction

The dynamical properties for delayed Hopfield neural networks have been extensively studied since they can be applied into pattern recognition, image processing, speed detection of moving objects, optimization problems and many other fields. To the best of our knowledge, up to now, there have been no papers published on the existence and stability of almost periodic solutions to neutral-type delay neural networks with time-varying delays in the leakage term on time scales.

Results

Conclusion