Open Access Research

Global exponential stability and existence of periodic solutions for delayed reaction-diffusion BAM neural networks with Dirichlet boundary conditions

Weiyuan Zhang1*, Junmin Li2 and Minglai Chen2

Author Affiliations

1 Institute of Mathematics and Applied Mathematics, Xianyang Normal University, Xianyang, 712000, China

2 School of Science, Xidian University, Xi’an, Shaanxi, 710071, China

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Boundary Value Problems 2013, 2013:105  doi:10.1186/1687-2770-2013-105

Published: 26 April 2013

Abstract

In this paper, both global exponential stability and periodic solutions are investigated for a class of delayed reaction-diffusion BAM neural networks with Dirichlet boundary conditions. By employing suitable Lyapunov functionals, sufficient conditions of the global exponential stability and the existence of periodic solutions are established for reaction-diffusion BAM neural networks with mixed time delays and Dirichlet boundary conditions. The derived criteria extend and improve previous results in the literature. A numerical example is given to show the effectiveness of the obtained results.

Keywords:
neural networks; reaction-diffusion; mixed time delays; global exponential stability; Poincaré mapping; Lyapunov functional