Bogdanov-Takens bifurcation in a predator-prey model

被引：12

作者：

Liu, Zhihua ^{[1
]}

Magal, Pierre ^{[2
,3
]}

Xiao, Dongmei ^{[4
]}

机构：

[1] Beijing Normal Univ, Sch Math Sci, Beijing 100875, Peoples R China

[2] Univ Bordeaux, IMB, UMR 5251, F-33400 Talence, France

[3] CNRS, IMB, UMR 5251, F-33400 Talence, France

[4] Shanghai Jiao Tong Univ, Dept Math, MOE LSC, Shanghai 200240, Peoples R China

来源：

ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2016年 / 67卷 / 06期

关键词：

Predator-prey model; Age structure; Normal forms; Non-densely defined; Bogdanov-Takens bifurcation; NORMAL FORMS; DIFFERENTIAL-EQUATIONS; HOPF-BIFURCATION; SYSTEM; OSCILLATIONS; STABILITY; DELAY;

D O I：

10.1007/s00033-016-0724-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we investigate a class of predator-prey model with age structure and discuss whether the model can undergo Bogdanov-Takens bifurcation. The analysis is based on the normal form theory and the center manifold theory for semilinear equations with non-dense domain combined with integrated semigroup theory. Qualitative analysis indicates that there exist some parameter values such that this predator-prey model has an unique positive equilibrium which is Bogdanov-Takens singularity. Moreover, it is shown that under suitable small perturbation, the system undergoes the Bogdanov-Takens bifurcation in a small neighborhood of this positive equilibrium.

引用

页数：29

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