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

作　　者：LIU Yan-wei LIU Xia 

机构地区：[1]Department of Mathematics, Zhoukou Normal University, Zhoukou 466001, China [2]College ofMathematics and Information Science, Henan Normal University, Xinxiang 453007, China

出　　处：《Chinese Quarterly Journal of Mathematics》2013年第2期234-240,共7页数学季刊（英文版）

基　　金：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：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.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 

分 类 号：O175.25[理学—数学]