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

Yahong Peng and Guoying Zhang

Mathematics and Computers in Simulation (MATCOM), 2020, vol. 170, issue C, 366-378

Abstract: 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.

Keywords: Predator–prey system; Reaction–diffusion; Nonlocal competition; Hopf bifurcation; Turing bifurcation (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:170:y:2020:i:c:p:366-378

DOI: 10.1016/j.matcom.2019.11.012

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