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

摘要

In this paper, we consider the almost periodic dynamics of an impulsivemultispecies Lotka-Volterra competition system with time delays on time scales.By establishing some comparison theorems of dynamic equations with impulses anddelays on time scales, a permanence result for the model is obtained.Furthermore, based on the permanence result, by studying the Lyapunov stabilitytheory of impulsive dynamic equations on time scales, we establish a criterionfor the existence and uniformly asymptotic stability of a unique positivealmost periodic solution of the system. Finally, we give an example to show thefeasibility of our main results and our example also shows that the continuoustime 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 thetime scale $\mathbb{T}=\mathbb{R}$ and the case of $\mathbb{Z}$.