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

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.