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

Chinese Quarterly Journal of Mathematics ›› 2013, Vol. 28 ›› Issue (2): 234-240.

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)

Abstract

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

CLC Number:

O175

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

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