带频率依赖染病率的密度依赖型寄生虫-宿主模型定性分析

Qualitative Analysis of Density-dependent Parasite-host Model with Frequency-dependent Infection Rate

对带频率依赖染病率的密度依赖型寄生虫-宿主模型进行了研究.首先,借助特征值理论,讨论了平衡态方程正常数平衡解的局部渐近稳定性.然后,利用局部分支理论,得出在(d■,(N~*,p~*))处可以产生局部分支,并且由全局分支理论可得该局部分支在一定条件下可以延拓成全局分支.

In this paper,the density-dependent parasite-host model with frequency-dependent morbidity is studied.First,the local asymptotic stability of the normal number equilibrium solution of the equilibrium equation is discussed by means of eigenvalue theory.Then,by the local bifurcation theory,it is concluded that a local bifurcation can be generated at(d1j,(N*,p*)),and the local bifurcation can be extended to a global branch under certain conditions by the global bifurcation theory.