一类比率依赖的Holling-Leslie捕食-食饵模型的全局分歧

计算机工程与应用 ›› 2012, Vol. 48 ›› Issue (17): 58-62.

一类比率依赖的Holling-Leslie捕食-食饵模型的全局分歧

杨文彬，李艳玲

陕西师范大学数学与信息科学学院，西安 710062

出版日期:2012-06-11 发布日期:2012-06-20

Global bifurcation of a class of ratio-dependent Holling-Leslie type predator- prey model

YANG Wenbin, LI Yanling

College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, China

Online:2012-06-11 Published:2012-06-20

摘要/Abstract

摘要： 研究了一类基于比率依赖的Holling-Leslie捕食-食饵扩散模型，运用分歧理论和Leray-Schauder度理论的知识，以捕食者的扩散系数为分歧参数，讨论了发自正常数平衡态的局部分支解的存在性，并将局部分歧延拓为整体分歧，从而得到非常数正平衡态存在的充分条件，给出了一维情况下整体分歧解的性态。

关键词: 比率依赖, Holling-Leslie, 分歧理论, Leray-Schauder度理论

Abstract: Based on the methods of the bifurcation theory and the Leray-Schauder degree theory, a class of ratio-
dependent Holling-Leslie type predator model, subject to homogeneous Neumann boundary condition, is investigated. The bifurcation from positive constant equilibrium is obtained by treating the diffusion coefficient of predator as bifurcation parameter. Through the use of local and global bifurcation theories, sufficient conditions for the existence of non-constant positive solution are derived. The fact that the global bifurcation joins up with infinity in the case of one-dimension is obtained.

Key words: ratio-dependent, Holling-Leslie, bifurcation theory, Leray-Schauder degree theory

杨文彬，李艳玲. 一类比率依赖的Holling-Leslie捕食-食饵模型的全局分歧[J]. 计算机工程与应用, 2012, 48(17): 58-62.

YANG Wenbin, LI Yanling. Global bifurcation of a class of ratio-dependent Holling-Leslie type predator- prey model[J]. Computer Engineering and Applications, 2012, 48(17): 58-62.

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