一类捕食食饵模型正解的整体分歧

Global Bifurcation of Positive Solutions to a Predator-Prey Model

摘要: 本文考察一类带Beddington-DeAngelie和Leslie反应项的捕食食饵模型。首先，采用全局分歧理论和特征值估计研究了平衡态共存解存在的充要条件，并刻画了共存解分支的全局结构。结果表明，当被捕食物种的生长率时，共存解分支有界，且连接了两半平凡的解分支；当时，共存解分支最终沿参数b趋于无穷(见图1)。其次，采用摄动理论分析了共存解分支的稳定性。

Abstract: This paper deals with a Prey-Predator model with Beddington-DeAngelis and Leslie functional response. First, sufficient and necessary conditions for coexistence solutions of the steady-state are discussed by the global bifurcation theory and the estimate of eigenvalues, and the structure of global bifurcation branch is investigated. It turns out that when  a  , the growth rate of prey, lies between  and , the continuum of nontrivial solution is bounded and joins two branches of semi-trivial solutions. This bifurcation branch goes to infinity with parameter b and a  when  is larger than (see Figure 1). Second, the stability for the coexistence solutions is given by perturbation technique.