Existence and global exponential stability of equilibrium for impulsive neural network models with generalized piecewise constant delay

Abstract

In this paper, we investigate the models of the impulsive cellular neural network with generalized constant piecewise delay (IDEGPCD). To guarantee the existence, uniqueness and global exponential stability of the equilibrium state, several new adequate conditions are obtained, which extend the results of the previous literature. The method is based on utilizing Banach’s fixed point theorem and a new IDEGPCD’s Gronwall inequality. The criteria given are easy to check and when the impulsive effects do not affect, the results can be extracted from those of the non-impulsive systems. Typical numerical simulation examples are used to show the validity and effectiveness of the proposed results. We end the paper with a brief conclusion.