Global attractivity of almost periodic solutions for competitive Lotka-Volterra diffusion system

TL;DR

This paper proves that under certain conditions, a two-patch competitive Lotka-Volterra system with diffusion has a unique, globally attractive almost periodic solution, ensuring predictable long-term dynamics.

Contribution

It establishes the existence, uniqueness, and global attractivity of almost periodic solutions for a diffusive Lotka-Volterra system using Lyapunov functions.

Findings

Existence of a unique almost periodic solution

Asymptotic stability of the solution

Global attractivity under moderate conditions

Abstract

In this paper, two competitive Lotka-Volterra populations in the two-patch-system with diffusion are considered. Each of the two spiecies can diffuse indepently and discretely between its in intrapatch and interpatch. By means of constructing Liapunov function, under moderate condition, the system has a unique almost periodic solution and which is asymptotically stable and globally attractive .