Periodicity of Nonautonomous Fuzzy Neural Networks with Reaction-Diffusion terms and Distributed Time Delays

Abstract

In this paper, the periodicity of a class of nonautonomous fuzzy neural networks with impulses, reaction-diffusion terms, and distributed time delays are investigated. By establishing an integro-differential inequality with impulsive initial conditions and time-varying coefficients, employing the $M$ -matrix theory, Poincar mappings, and fixed point theory, several new sufficient conditions to ensure the periodicity and global exponential stability of the formulated system are obtained. It is worthwhile to mention that our technical methods are practical, in the sense that all new stability conditions are stated in simple algebraic forms, and an optimization method is provided to estimate the exponential convergence rate, so their verification and applications are straightforward and convenient. The validity and generality of our methods are illustrated by two numerical examples.