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具有比率依赖和年龄结构的捕食食饵系统的分支研究
乔梅红^1,2, 刘安平¹
1.中国地质大学(武汉)数理学院, 湖北武汉 430074;2.华中科技大学数学中心, 湖北武汉 430074

摘要:

本文研究了具有比率依赖的捕食食饵的分支问题.利用线性特征方程的方法，获得了方程解的稳定性结果，得到了Hopf分支的方向和稳定性的充分条件.

关键词: 时滞捕食食饵模型稳定性 Hopf分支

DOI：

分类号:O175.13

基金项目:Supported by the Basic Research Program of Hubei Province(2014CFB898); NSFC (11571326; 11601496).

BIFURCATION IN A RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH STAGE-STRUCTURED IN THE PREY POPULATION

QIAO Mei-hong^1,2, LIU An-ping¹

1.School of Mathematics & Physics, China University of Geoscience, Wuhan 430074, China;2.Center for Mathematical Sciences, Huazhong University of Science and Technology, Wuhan 430074, China

Abstract:

In this paper, we study the bifurcation of ratio-dependent predator-prey system. By using the characteristic equation of the linearized system and the center manifold theorem, we derive the stability of the system and direction of the Hopf bifurcation.

Key words: time delay predator-prey model stability Hopf bifurcation