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

作　　者：常文丛[1] 聂华[1] Wencong Chang;Hua Nie(College of Mathematics and Information Science,Shaanxi Normal University,Xi’an)

机构地区：[1]陕西师范大学数学与信息科学学院,西安

出　　处：《理论数学》2012年第4期226-236,共11页Pure Mathematics

基　　金：国家自然科学基金(11001160);陕西省自然科学基础研究计划(2011JQ1015)。

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a∈{λ1,λ1+a2/k}时,共存解分支有界,且连接了两半平凡的解分支;当a≥λ1+a2/k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。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 λ1 and λ1 +a2/k , the continuum of nontrivial solution is bounded and joins two branches of semi-trivial solutions. This bifurcation branch goes to infinity with parameter b when a is larger than λ1 +a2/k (see Figure 1). Second, the stability for the coexistence solutions is given by perturbation technique.

关 键 词：捕食—食饵模型 分歧理论 摄动理论 正平衡解 

分 类 号：O1[理学—数学]