Almost Automorphic Solutions for Fuzzy Cohen-Grossberg Neural Networks with Mixed Time Delays

Yongkun Li,Xiaofang Meng,Xuemei Zhang

doi:10.1155/2015/812670

Yongkun Li, Xiaofang Meng + Show 1 more

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https://doi.org/10.1155/2015/812670

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Abstract

This paper is concerned with the problem of almost automorphic solutions of a class of fuzzy Cohen-Grossberg neural networks with mixed time delays and variable coefficients. Based on inequality analysis techniques and combining the exponential dichotomy with fixed point theorem, some sufficient conditions for the existence and global exponential stability of almost automorphic solutions are obtained. Finally, a numerical example is given to show the feasibility of our results.

Highlights

In recent years, neural networks have been extensively studied due to their important applications in many areas such as function approximation, pattern recognition, associative memory, and combinatorial optimization
The dynamics of neural networks, especially the existence of periodic solutions, antiperiodic solutions, and almost periodic solutions to neural networks, has been extensively investigated and a large number of criteria on the stability of neural networks have been discussed in the literature [1,2,3,4,5]
To the best of our knowledge, there is no paper published on the existence and stability of almost automorphic solutions for fuzzy neural networks with time delays

Summary

Introduction

Neural networks have been extensively studied due to their important applications in many areas such as function approximation, pattern recognition, associative memory, and combinatorial optimization. Some results on stability and other behaviors have been derived for fuzzy neural networks with or without time delays (see [14,15,16,17,18,19,20,21,22]). To the best of our knowledge, there is no paper published on the existence and stability of almost automorphic solutions for fuzzy neural networks with time delays. Motivated by the above discussion, in this paper, we propose a class of fuzzy Cohen-Grossberg neural networks with mixed time delays and variable coefficients as follows: xi󸀠 (t) = −ai (xi (t)).

Preliminary

Main Results

An Example