Exponential stability of periodic solution for a memristor-based inertial neural network with time delays

Abstract

In this paper, exponential stability of periodic solution for an inertial neural network is studied. Different from most research on inertial neural networks, the model in this paper is based on memristors and is involved with periodic solutions. In order to simplify the difficulty in dealing with inertial terms and constructing Lyapunov functions, the inertial neural network in this paper is transformed into a suitable neural network with enhanced characteristics by using appropriate variable transformation method. Under the Lyapunov stability theory and Leary-Schauder alternative theorem, we prove the existence and global exponential stability of the periodic solution for the inertial neural network under mild conditions. At last, the feasibility of the theoretical conclusions is illustrated by some numerical examples.