一类脉冲种群竞争模型的周期解及其稳定性  

Periodic Solutions and Stability Analysis of a Periodic Impulsive Species Model

作　　者：李泽妤[1] 窦家维[2] 宋国华[1] 

机构地区：[1]北京建筑工程学院基础部,北京100044 [2]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《中北大学学报（自然科学版）》2008年第1期8-11,共4页Journal of North University of China(Natural Science Edition)

基　　金：北京市教育委员会科技发展计划面上项目(KM200410016010);北京市委组织部优秀人才资助项目(2004D0501704);北京建筑工程学院博士启动基金

摘　　要：研究了在周期变化环境中具有Holling-Tanner型功能性反应的两种群竞争模型.模型由一个周期脉冲常微分方程组描述.利用不动点方法研究了系统的平凡及半平凡周期解的稳定性,获得了周期解为指数稳定的一组容易验证的充要条件,该方法可以推广到其他微分方程周期解的稳定性的研究中.The mathematical model of two competitive species with Holling-Tanner function reaction in a periodically changing environment is investigated. The model is described by a class of periodic impulsive ordinary differential equations. The existence and the stability of periodic solutions are discussed by a fixed point method. The necessary and sufficient conditions of the periodic solutions being exponential asymptotical stability are obtained. The method used here can be applied to the stability study of the periodic solutions of other differential equations.

关 键 词：脉冲微分方程 周期解 指数稳定 

分 类 号：O175.1[理学—数学]