疾病在食饵中传播的具有时滞的捕食被捕食模型的分析  

Analysis of an Prey-Predator Model with Delay and the Disease in the Prey

作　　者：王晓庆[1] 薛亚奎[1] 

机构地区：[1]中北大学数学系,山西太原030051

出　　处：《数学的实践与认识》2010年第17期251-256,共6页Mathematics in Practice and Theory

基　　金：国家自然科学基金(10471040);山西省自然科学基金(2009011005-1)

摘　　要：研究了一个疾病在食饵中传播的捕食与被捕食模型.在未引入时滞时,利用Routh-Hurwitz定理证明了正平衡点的局部渐近稳定性.在引入时滞后,主要讨论了正平衡点的稳定性,得到了当经过一系列临界条件时发生Hopf分支.In this paper,we analyze a predator-prey model with disease in the prey.When the time dalay is zero,we obtain the sufficient conditions of locally asymptotic stability of the positive equilibrium by the Routh-Hurwitz criterion.It is also shown that the time delay cause the stable equilibrium to become unstable,and Hopf bifurcation occur when the delay T passess through a sequence of critical values.

关 键 词：时滞 HOPF分支 捕食与被捕食 局部渐近稳定 

分 类 号：O175[理学—数学]