一类食饵带有避难的比率依赖型捕食系统的分支和极限环

数学季刊 ›› 2013, Vol. 28 ›› Issue (2): 234-240.

一类食饵带有避难的比率依赖型捕食系统的分支和极限环

1. Department of Mathematics, Zhoukou Normal University2. College of Mathematics and Information Science, Henan Normal University

收稿日期:2011-10-11 出版日期:2013-06-30 发布日期:2023-03-02
作者简介:LIU Xia(1980-), female, native of Zhoukou, Henan, a lecturer of Henan Normal University, Ph.D., engages in dynamical system.
基金资助:
Supported by the NNSF of China(11126284)； Supported by the NSF of Department of Education of Henan Province(12A110012)； Supported by the Young Scientific Research Foundation of Henan Normal University(1001)

Bifurcation and Limit Cycle of a Ratio-dependent Predator-prey System with Refuge on Prey

1. Department of Mathematics, Zhoukou Normal University2. College of Mathematics and Information Science, Henan Normal University

Received:2011-10-11 Online:2013-06-30 Published:2023-03-02
About author:LIU Xia(1980-), female, native of Zhoukou, Henan, a lecturer of Henan Normal University,Ph.D., engages in dynamical system.
Supported by:
Supported by the NNSF of China(11126284)； Supported by the NSF of Department of Education of Henan Province(12A110012)； Supported by the Young Scientific Research Foundation of Henan Normal University(1001)

摘要/Abstract

摘要： Influences of prey refuge on the dynamics of a predator-prey model with ratio-dependent functional response are investigated. The local and global stability of positive equilibrium of the system are considered. Theoretical analysis indicates that constant refuge leads to the system undergo supercritical Hopf bifurcation twice with the birth rate of prey species changing continuously.

关键词: ratio-dependent, Hopf bifurcation, prey refuge, limit cycle

Abstract: Influences of prey refuge on the dynamics of a predator-prey model with ratio-dependent functional response are investigated. The local and global stability of positive equilibrium of the system are considered. Theoretical analysis indicates that constant refuge leads to the system undergo supercritical Hopf bifurcation twice with the birth rate of prey species changing continuously.

Key words: ratio-dependent, Hopf bifurcation, prey refuge, limit cycle

中图分类号:

O175

刘艳伟, 刘霞. 一类食饵带有避难的比率依赖型捕食系统的分支和极限环[J]. 数学季刊, 2013, 28(2): 234-240.

LIU Yan-wei, LIU Xia. Bifurcation and Limit Cycle of a Ratio-dependent Predator-prey System with Refuge on Prey[J]. Chinese Quarterly Journal of Mathematics, 2013, 28(2): 234-240.

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