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.
出处
《数学的实践与认识》
CSCD
北大核心
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)