具有时滞和阶段结构的L-V竞争系统的稳定性分析  

Stability Analysis of a Competitive Lotka-Volterra System with Time Delays and Stage Structure

作　　者：郑重武[1] 焦守文[1,2] 张凤琴[1,2] 

机构地区：[1]运城学院应用数学系,运城044000 [2]中北大学理学院数学系,太原030051

出　　处：《工程数学学报》2011年第6期839-844,共6页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(11071283);山西省自然科学基金(2009011005-3)~~

摘　　要：具有阶段结构的L-V时滞竞争系统是一类重要的反映种群竞争关系的生态系统,它考虑了时滞效应以及不同阶段幼体和成体竞争能力差异.本文讨论了一类具有两个时滞和阶段结构的L-V竞争系统平衡点的局部稳定性以及正平衡点的全局稳定性.根据Hurwitz判据,我们得到了该系统平衡点局部稳定的条件;依据单调系统的相关理论以及迭代法,我们获得了正平衡点全局稳定的条件,并得出时滞存在没有影响正平衡态全局稳定的重要结论.The Lotka-Volterra delay competition systems with stage structure is an important kind of ecosystems which reflect competition relationship among species,the system considers delay effects and the competition ability difference between larval and adult at different stages.In this paper,the local stability and the global stability of equilibria for the competitive Lotka-Volterra system with two delays and a stage structure are discussed by utilizing the Hurwitz criterion.Furthermore,the suffcient conditions for the local stability of equilibria of the competitive Lotka-Volterra system are established,and the suffcient conditions for the global stability of the positive equilibrium of the system are obtained with the theory of monotonic systems and the iteration method.It is shown that delays do not affect the stability of the positive equilibrium.

关 键 词：L-V竞争系统 时滞 阶段结构 稳定性 迭代法 

分 类 号：O175.13[理学—数学]