Existence and stability of periodic solutions for impulsive fuzzy BAM Cohen-Grossberg neural networks on time scales

Qianhong Zhang,Shaohong Cai

doi:10.1186/s13662-016-0762-1

Qianhong Zhang, Shaohong Cai

Open Access

https://doi.org/10.1186/s13662-016-0762-1

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Abstract

This paper is concerned with the existence and global exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen-Grossberg BAM neural networks on time scales. Applying the method of coincidence degree and constructing some suitable Lyapunov functional, we obtain some sufficient conditions for the existence and global exponential stability of periodic solutions for a kind of impulsive fuzzy Cohen-Grossberg BAM neural networks on time scales. Moreover, we give an example to illustrate the results obtained.

Highlights

In recent years, Cohen and Grossberg BAM neural networks have been extensively studied and applied in many different fields such as associative memory, signal processing, and some optimization problems
Many results for the existence of their periodic solutions and the exponential convergence properties for Cohen-Grossberg neural networks have been reported in the literature
Researchers have found that fuzzy cellular neural networks (FCNNs) and fuzzy Cohen-Grossberg neural networks are useful in image processing, and some results have been reported on stability, periodicity, and antiperiodicity

Summary

Introduction

Cohen and Grossberg BAM neural networks have been extensively studied and applied in many different fields such as associative memory, signal processing, and some optimization problems. It is troublesome to study the existence and stability of periodic solutions for continuous and discrete systems, respectively. Βji(t)fj (yj(t i(xi(tk)) = Iik(xi(tk)), k αji (t)fj(yj (t τji)) + Ei(t)], t ∈ T+, N, i = , , . Throughout this paper, we make the following assumptions: (A ) Ei, Fj, αji, βji, pij, qij ∈ C(T, R) are ω-periodic functions, τji, σij ∈ R+, i = , , .

Results

Conclusion