عنوان مقاله [English]
In this paper, we consider a diffusive predator-prey model, in which the prey population lives in groups and has a social behavior. We show that Hopf bifurcation and the existence of a center manifold may occur.
The linear stability analysis shows that a Hopf bifurcation occurs in the corresponding homogeneous system.
Next, we study the effect of diffusion parameters on homogeneous dynamics.
By choosing a proper bifurcation parameter, we prove that a Hopf bifurcation occurs in the nonhomogeneous system. We compute the normal form of this bifurcation up to the third order and obtain the direction of the Hopf bifurcation. Finally, we provide numerical simulations to illustrate our analytical findings.