一类捕食-食饵模型分歧解的局部稳定性和全局分歧

摘要

Discussed in this paper are the properties of the bifurcation solutions for a kind of predatorprey model between two species with the Holling type Ⅱ functional response, which incorporates a prey refuge under the inhomogeneous Dirichlet boundary conditions. By employing the local bifurcation theory and local stability theory, the condition for the local stability of bifurcation solutions to this system is derived. In addition, the conclusion that a local bifurcation can be extended to a global bifurcation is obtained by virtue of the degree theory.%本文利用局部分歧理论和局部稳定性理论,讨论了一类具有避难所的两物种间的捕食-食饵模型在非齐次Dirichlet边界条件下分歧解的性质,其功能反应函数为Holling Ⅱ型.利用局部分歧和局部稳定性理论给出了分歧解局部稳定的条件;同时利用度理论得到了局部分歧可以延拓到整体分歧的结论.