Dynamics analysis of a predator-prey model with herd behavior and nonlocal prey competition

摘要

Nonlocal reaction-diffusion model is an important area to study the dynamics of the individuals which compete for resources. In this paper, we consider a predator-prey model with herd behavior and nonlocal prey competition. We investigate the effects of nonlocal competition on dynamics of the system in the bounded region when the kernel function takes 1/(|Ω|) and derive the conditions that the nonlocal system undergoes Hopf bifurcation and Turing bifurcation. Then we discuss the influence of nonlocal competition on the stability of the positive constant equilibrium in unbounded region when the kernel function takes a step kernel function. Our result shows that nonlocal competition can destabilize the stability of the predator-prey system.