Exponential stability of delayed bidirectional associative memory neural networks with reaction diffusion terms

Abstract

This article considers a class of delayed bi-directional associative memory (BAM) neural networks with reaction diffusion terms and delays. We obtain some simple criteria ensuring the existence and uniqueness of the equilibrium and its global exponential stability by applying homeomorphism mapping, constructing a new Lyapunov functional and inequality techniques. These criteria are independent of delays and posses infinitely adjustable real parameters, which improve and extend some recent results [J. Cao and M. Dong, “Exponential stability of delayed bidirectional associative memory networks”, Appl. Math. Comput., 135, pp. 105–112, 2003; J. Cao and L. Wang, “Exponential stability and periodic oscillatory solution in BAM networks with delays”, IEEE Trans. Neural Networ., 13, pp. 457–463, 2002; Q. Song and J. Cao, “Global exponential stability and existence of periodic solutions in BAM networks with delays and reaction-diffusion terms”, Chaos Soliton. Fract., 23, pp. 421–430, 2005.] and have an important instructional significance in the designs and applications of bidirectional associative memory neural networks.