Pseudo-Almost Periodic Solution on Time-Space Scales for a Novel Class of Competitive Neutral-Type Neural Networks with Mixed Time-Varying Delays and Leakage Delays

Abstract

A competitive neural network model was proposed to describe the dynamics of cortical maps in which, there exist two memories: long-term and short-term. In this paper, we investigate the existence and the exponential stability of the pseudo-almost periodic solution of a system of equations modeling the dynamics of neutral-type competitive neural networks with mixed delays in the time-space scales for the first time. The mixed delays include time-varying delays and continuously distributed ones. Based on contraction principle and the theory of calculus on time-space scales, some new criteria proving the convergence of all solutions of the networks toward the unique pseudo-almost periodic solution are derived by using the ad-hoc Lyapunov–Krasovskii functional. Finally, numerical example with graphical illustration is given to confirm our main results.