Stepanov-like Weighted Pseudo-Almost Automorphic Solutions on Time Scales for a Novel High-order BAM Neural Network with Mixed Time-varying Delays in the Leakage Terms

TL;DR

This paper introduces a new class of oscillatory solutions called Stepanov-like weighted pseudo-almost automorphic functions on time scales, and applies them to analyze the stability of high-order BAM neural networks with delays.

Contribution

It defines Stepanov-like weighted pseudo-almost automorphic solutions on time scales and establishes their existence and stability in high-order BAM neural networks with mixed delays.

Findings

Existence of Stepanov-like weighted pseudo-almost automorphic solutions proven.

Exponential stability criteria for the solutions established.

Numerical example confirms the theoretical results.

Abstract

We first propose the concept of Stepanov-like weighted pseudo-almost automorphic on time-space scales and we apply this type of oscillation to high-order BAM neural networks with mixed delays. Then, we study the existence and exponential stability of Sp-weighted pseudo almost automorphic on time-space scales solutions for the suggested system. Some criteria assuring the convergence are proposed. Our method is mainly based on the Banachs fixed point theorem, the theory of calculus on time scales and the Lyapunov-Krasovskii functional method. Moreover, a numerical example is given to show the effectiveness of the main results.