时滞在具有Ivlev型功能反应函数的捕食者-食饵扩散系统中的作用

摘要/Abstract

摘要：

该文研究了时滞对一个带Neumann边值的捕食者-食饵的反应扩散系统的影响. 通过对特征根的分析, 讨论了非负平衡解的稳定性和Hopf分支的存在性. 应用规范型方法和中心流形理论, 文章讨论了Hopf分支周期解的稳定性和分支方向.

关键词: 捕食者-食饵, 时滞, Ivlev型功能反应项, Hopf分支, 周期解

Abstract:

A delayed diffusive predator-prey system with Ivlev-type predator functional response subject to Neumann boundary conditions is considered. The stability of nonnegative equilibria and existence of Hopf bifurcation are obtained by analyzing the distribution of the eigenvalues. By the theory of normal form and center manifold, an explicit algorithm for determining the stability and direction of periodic solution bifurcating from Hopf bifurcation is derived.

Key words: Prey-predator, Delay, Ivlev-type functional response, Hopf bifurcation, Periodic solutions

中图分类号:

35B32

王雪臣, 魏俊杰. 时滞在具有Ivlev型功能反应函数的捕食者-食饵扩散系统中的作用[J]. 数学物理学报, 2014, 34(2): 234-250.

WANG Xue-Chen, WEI Jun-Jie. The Effect of Delay on a Diffusive Predator-Prey System with Ivlev-Type Functional Response[J]. Acta mathematica scientia,Series A, 2014, 34(2): 234-250.

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