Stability And Bifurcation Analysis Of A Predator-Prey Model

In this paper we study the stability,Hopf bifurcation,and Turing instability of a class of predator-prey model with Holling-? type functional response functions and non-linear harvesting terms.First,we proved the stability of the non-negative equilibrium point through the linearization method.Second,using the Poincare-Andronov Hopf branch theorem,we obtained the existence,direction,and stability of Hopf bifurcation.Then,using matlab software to obtain The results are numerically simulated.Finally,we discuss the system after adding the diffusion term:...