Dynamical analysis on prey refuge in a predator-prey model with square root functional response

In this paper, we consider a predator-prey model with square root functional response and prey refuge.The study reveals that the dynamical behavior near the origin of the model is subtle and interesting.We also show that the model undergoes Transcritical bifurcation and Hopf bifurcation.Numerical simulations not only illustrate our results, but also exhibit richer dynamical behaviors of the model than those with Holling II type functional response.Taking prey refuge as control variable, it is feasible to decrease predation rate and then control predator density properly so as to avoid two of population extinction and promote coexistence.