The Predator-Prey Model With Holling-? Functional Response Function

The present paper is concerned with the ratio-dependent predator-prey diffusion system.In order to investigate the stability of the positive constant steady state and Hopf bifurcation,the system at the positive constant steady state is linearized and the associated characteristic equation is analyzed,and the asymptotic stability of the positive constant steady state is obtained.It is proved that the positive constant steady state loses stability as the delays cross certain values.We also obtain the existence of Hopf bifurcation.