Persistence and Almost Periodic Solutions in a Model of Plankton Allelopathy with Impulsive Effects

DOI：10.3770/j.issn:2095-2651.2016.02.009

 作者 单位 徐丽君 攀枝花学院数学与计算机学院, 四川 攀枝花 617000 李亚芹 昆明学院数学系, 云南 昆明 650214 杨永洪 云南民族大学预科学院, 云南 昆明 650031 张天伟 昆明理工大学城市学院, 云南 昆明 650051

利用脉冲微分方程的对比定理以及李雅普诺夫函数法,我们研究了一类具有脉冲效应的浮游生物模型的持久性以及概周期解.文中所得结论改进了以往的研究成果.文中所用的研究方法可以用来研究其他带有脉冲的生物数学模型的持久性以及概周期解.最后,我们总结阐述了脉冲如何影响模型的持久性,概周期解以及一致渐进稳定性.

This paper is concerned with an almost periodic model of plankton allelopathy with impulsive effects. By using the comparison theorem and the Lyapunov method of the impulsive differential equations, sufficient conditions which guarantee the permanence and existence of a unique uniformly asymptotically stable positive almost periodic solution of the model are obtained. The main results in this paper improve the work in recent years. And the method used in this paper provides a new method to study the permanence, uniform asymptotical stability and almost periodic solution of the models with impulsive perturbations in biological populations. An example and numerical simulations are provided to illustrate the main results of this paper. Finally, a conclusion is also given to discuss how the impulsive effects influence the permanence, almost periodic solutions and uniform asymptotical stability of the model.