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

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.