Bifurcation analysis of a diffusive predator-prey model with fear effect

In this paper, a diffusive predator-prey system with fear factor response subject to Neumann boundary conditions is considered. Bifurcations at the boundary equilibria of the corresponding ODE are confirmed by Sotomayor's theorem. Detailed bifurcation analysis shows that the reaction-diffusion system undergoes Hopf bifurcation and steady-state bifurcation. The bifurcation direction and the stability of the bifurcating periodic solutions are also given. Finally, numerical simulation results are carried out to verify the theoretical results.