Spatiotemporal Dynamics Induced by Nonlocal Competition in a Diffusion Predator-Prey System with Habitat Complexity

Abstract

In this paper, we study a delayed diffusive predator-prey model with nonlocal competition in prey and habitat complexity. The local stability of coexisting equilibrium are studied by analyzing the eigenvalue spectrum. Time delay inducing Hopf bifurcation is investigated by using time delay as bifurcation parameter. We give some conditions for determining the bifurcation direction and the stability of the bifurcating periodic solution by utilizing the normal form method and center manifold theorem. Our results suggest that only nonlocal competition and diffusion together can induce stably spatial inhomogeneous bifurcating periodic solutions.

Spatiotemporal dynamics in a delayed diffusive predator–prey system with nonlocal competition in prey and schooling behavior among predators

“…In [18], Geng et al studied Hopf, Turing, double-Hopf, and Turing-Hopf bifurcations of a diffusive predator-prey model with nonlocal competition. In [19][20][21][22], all the authors show that the nonlocal competition may induce stably spatially inhomogeneous bifurcating periodic solutions, which is different from the model without nonlocal competition. Inspired by the above work, we want to analyze the effect of nonlocal competition, time delay, and spatial diffusion on the model (1.1).…”