Existence and exponential stability of anti-periodic solutions for interval general bidirectional associative memory neural networks with multiple delays

Deng Ding,Jianzhong Feng,Songbo Hu,Xiaofei Li

doi:10.1186/s13662-016-0882-7

Abstract

In this article, we will consider the a class of interval general bidirectional associative memory (BAM) neural networks with multiple delays. Based on the fundamental solution matrix of coefficients, inequality technique and Lyapunov method, we derive a series of sufficient conditions to ensure the existence and exponential stability of anti-periodic solutions of the neural networks with multiple delays. Our findings are new and complement some previously known studies.

Highlights

As is well known, neural networks have been effectively applied in numerous disciplines such as pattern recognition, classification, associative memory, optimization, signal and image processing, parallel computation, nonlinear optimization problems, and so on
With the help of the continuation theorem of coincidence degree theory and constructing some suitable Lyapunov functionals, the authors discussed the existence and global exponential stability of periodic solutions for system ( . )
Inspired by the idea and work above, we will investigate the anti-periodic solutions of the following interval general bidirectional associative memory (BAM) neural networks with multiple delays: xi (t ) dt yj (t) dt sji (t)fj[xj(t), yj(t ci (t), m i=

Summary

Introduction

Neural networks have been effectively applied in numerous disciplines such as pattern recognition, classification, associative memory, optimization, signal and image processing, parallel computation, nonlinear optimization problems, and so on (see [ – ]). With the help of the continuation theorem of coincidence degree theory and constructing some suitable Lyapunov functionals, the authors discussed the existence and global exponential stability of periodic solutions for system It is meaningful to discuss the existence and stability of anti-periodic solutions of neural networks.

Results

Conclusion