Hopf Bifurcation in a Delay-Diffusive Holling-Tanner Predator-Prey Model with Smith Growth

In this paper, we chiefly take the stability and Hopf bifurcation of a diffusive Holling-Tanner predator-prey model with Smith growth and delay into consideration. Firstly, we analyze the local stability of the system, the existence of Hopf bifurcation in the co-existence of the equilibrium process. Furthermore, with help of normal formal theory and center manifold theorem, the stability of bifurcating periodic solutions and the direction of Hopf bifurcation are established. Finally, we prove the effectiveness of the theoretical analysis through numerical simulations, and rich dynamical behavior of the diffusive predator-prey system.