徐丽君,李亚芹,杨永洪,张天伟.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[J].数学研究及应用,2016,36(2):201~212
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
Persistence and Almost Periodic Solutions in a Model of Plankton Allelopathy with Impulsive Effects
投稿时间:2014-12-03  最后修改时间:2015-03-04
DOI:10.3770/j.issn:2095-2651.2016.02.009
中文关键词:  概周期解  持久性  一致渐进稳定性  脉冲  浮游生物
英文关键词:almost periodic solution  permanence  uniformly asymptotically stable  impulse  plankton allelopathy
基金项目:云南省教育厅科学研究基金项目(Grant No.2014Y388).
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 
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中文摘要:
      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.
英文摘要:
      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.
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