Asymptotical stability of almost periodic solution for an impulsive multispecies competition-predation system with time delays on time scales

TL;DR

This paper investigates the long-term behavior of an impulsive multispecies competition-predation model with delays on time scales, establishing conditions for the existence and stability of almost periodic solutions.

Contribution

It introduces new comparison theorems and stability criteria for impulsive dynamic equations on time scales, covering both continuous and discrete cases.

Findings

Proved the existence of a unique positive almost periodic solution.

Established criteria for asymptotic stability of solutions.

Demonstrated the equivalence of continuous and discrete time dynamics.

Abstract

In this paper, we consider the almost periodic dynamics of an impulsive multispecies Lotka-Volterra competition system with time delays on time scales. By establishing some comparison theorems of dynamic equations with impulses and delays on time scales, a permanence result for the model is obtained. Furthermore, based on the permanence result, by studying the Lyapunov stability theory of impulsive dynamic equations on time scales, we establish a criterion for the existence and uniformly asymptotic stability of a unique positive almost periodic solution of the system. Finally, we give an example to show the feasibility of our main results and our example also shows that the continuous time system and its corresponding discrete time system have the same dynamics. Our results of this paper are completely new even if for both the case of the time scale $\mathbb{T}=\mathbb{R}$ and the case of $\mathbb{Z}$.