Weighted pseudo-almost periodic functions on time scales with applications to cellular neural networks with discrete delays

TL;DR

This paper introduces weighted pseudo-almost periodic functions on time scales, explores their properties, and applies these concepts to establish the existence and stability of solutions in cellular neural networks with delays.

Contribution

It presents a novel concept of weighted pseudo-almost periodic functions on time scales and applies it to analyze neural networks with discrete delays.

Findings

Existence of weighted pseudo-almost periodic solutions for linear dynamic equations.

Global exponential stability of solutions in cellular neural networks.

New theoretical framework for functions on time scales.

Abstract

In this paper, we first propose a concept of weighted pseudo-almost periodic functions on time scales and study some basic properties of weighted pseudo-almost periodic functions on time scales. Then, we establish some results about the existence of weighted pseudo-almost periodic solutions to linear dynamic equations on time scales. Finally, as an application of our results, we study the existence and global exponential stability of weighted pseudo-almost periodic solutions for a class of cellular neural networks with discrete delays on time scales. The results of this paper are completely new.