The dynamic behavior of predator-prey diffusion system with fear effects. (Chinese. English summary) Zbl 07802091

Li, Muzi; Wei, Chunjin

Acta Math. Appl. Sin. 46, No. 6, 879-894 (2023).

Summary: In this paper, we investigate the dynamic behavior of a predator-prey diffusion system with fear effects. For the local model, the existence and stability of the nonnegative equilibria of the system are obtained. For reaction-diffusion system, the existence condition of Hopf bifurcation and Turing bifurcation are studied. In the case of Hopf bifurcation, by using the center manifold theory and normal form method, we establish the bifurcation direction and stability of bifurcating periodic solutions. Finally, the correctness of the theoretical results is verified by numerical simulations, which shows that the system has rich dynamic behavior.

MSC:

35B32	Bifurcations in context of PDEs
35B36	Pattern formations in context of PDEs
35K57	Reaction-diffusion equations
92D25	Population dynamics (general)

Keywords:

predator-prey system; fear factor; Hopf bifurcation; Turing bifurcation