时间尺度上具有时滞的脉冲多种群竞争-捕食系统的殆周期解的渐近稳定性
Asymptotical stability of almost periodic solution for an impulsive multispecies competition-predation system with time delays on time scales
摘要：
本文研究了时间尺度上具有时滞的脉冲多种群Lotka-Volterra竞争系统的概周期动力学.通过建立时间尺度上具有脉冲和时滞的动力学方程的比较定理，得到了该模型的持久性结果。在此基础上，通过研究时间尺度上脉冲动力方程的李雅普诺夫稳定性理论，建立了该系统唯一正殆周期解的存在性和一致渐近稳定性的判据.最后，我们给出一个例子来说明我们的主要结果的可行性和我们的例子也表明，连续时间系统和它对应的离散时间系统具有相同的动力学。本文的结果是完全新的，即使对于时间尺度$\mathbb{T}=\mathbb{R}$和$\mathbb{Z}$的情况。
英文摘要：
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 $\mathbb{Z}$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
