一类具有时滞的传染病模型的稳定性分析  

Stability Analysis of an Eco-Epidemic Model with Delay

作　　者：马剑[1] 张春蕊[1] 

机构地区：[1]东北林业大学数学系,黑龙江哈尔滨150040

出　　处：《生物数学学报》2007年第3期455-464,共10页Journal of Biomathematics

基　　金：中国博士后科学基金(2004036108)部分资助;东北林业大学优秀创新项目资助

摘　　要：研究了一类具有时滞的传染病生物模型.首先研究了该模型的线性稳定性,并给出了一列Hopf分支值,然后利用中心流形定理和正规型方法,给出了确定分支周期解的分支方向与稳定性的计算公式.A three-dimensional eco-epidemic model with delay is considered. Firstly, the linear stability of the model is studied. It is found that there exist Hopf bifurcations when the delay passes a sequence of critical values. Then the explicit algorithm for determining the direction of the Hopf bifurcations and the stability of the bifurcating periodic solutions are derived by using the normal form method and center manifold theorem.

关 键 词：时滞微分方程 稳定性 传染病模型 HOPF分支 

分 类 号：O175.14[理学—数学]