Permanence and almost periodic solution of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales

TL;DR

This paper investigates the long-term behavior and existence of almost periodic solutions in a multispecies Lotka-Volterra mutualism model with time-varying delays on time scales, using dynamic inequalities, hull theory, and Lyapunov functionals.

Contribution

It extends existing results by establishing permanence and criteria for almost periodic solutions in a generalized time scales setting.

Findings

Established permanence of the model.

Derived criteria for existence and uniqueness of almost periodic solutions.

Provided an example illustrating the main results.

Abstract

In this paper, we consider the almost periodic dynamics of a multispecies Lotka-Volterra mutualism system with time varying delays on time scales. By establishing some dynamic inequalities on time scales, a permanence result for the model is obtained. Furthermore, by means of the almost periodic functional hull theory on time scales and Lyapunov functional, some criteria are obtained for the existence, uniqueness and global attractivity of almost periodic solutions of the model. Our results complement and extend some scientific work in recent years. Finally, an example is given to illustrate the main results.