Pseudo almost periodic solutions for neutral type high-order Hopfield neural networks with mixed time-varying delays and leakage delays on time scales

TL;DR

This paper establishes conditions for the existence and stability of pseudo almost periodic solutions in high-order neutral Hopfield neural networks with delays on time scales, unifying continuous and discrete cases.

Contribution

It introduces new sufficient conditions for stability and existence of solutions in neural networks with mixed delays on arbitrary time scales, combining continuous and discrete analysis.

Findings

Conditions for existence of pseudo almost periodic solutions

Global exponential stability results

Continuous and discrete-time neural networks exhibit similar behaviors

Abstract

In this paper, a class of neutral type high-order Hopfield neural networks with mixed time-varying delays and leakage delays on time scales is proposed. Based on the exponential dichotomy of linear dynamic equations on time scales, Banach's fixed point theorem and the theory of calculus on time scales, some sufficient conditions are obtained for the existence and global exponential stability of pseudo almost periodic solutions for this class of neural networks. Our results are completely new. Finally, we present an example to illustrate our results are effective. Our example also shows that the continuous-time neural network and its discrete-time analogue have the same dynamical behaviors for the pseudo almost periodicity.