Dynamics of delayed cellular neural networks in the Stepanov pseudo almost automorphic space

Abstract

<p style='text-indent:20px;'>Pseudo almost automorphy (PAA) is a natural generalization of Bochner almost automorphy and Stepanov almost automorphy. Therefore, the results of the existence of PAA solutions of differential equations are few, and the results of the existence of pseudo almost automorphic solutions of difference equations are rare. In this work, we are concerned with a model of delayed cellular neural networks (CNNs). The delays are considered in varying-time form. By the Banach's fixed point theorem, Stepanov like PAA, and constructing a novel Lyapunov functional, we fixed a sufficient criteria that agreement the existence and the Stepanov-exponential stability of Stepanov-like PAA solution of this model of CNNs are obtained. In addition, a numerical example and simulations are performed to verify our theoretical results.</p>