Spatial nonhomogeneous periodic solutions induced by nonlocal prey competition in a diffusive predator-prey model

TL;DR

This paper demonstrates that nonlocal prey competition in a diffusive predator-prey model can induce stable, spatially nonhomogeneous periodic solutions through Hopf bifurcation, highlighting effects absent in local models.

Contribution

It establishes the existence of spatial nonhomogeneous periodic solutions caused by nonlocal prey competition in a predator-prey model, which is a novel finding.

Findings

Spatial nonhomogeneous periodic solutions exist due to nonlocal prey competition.

The positive steady state can lose stability via Hopf bifurcation.

Bifurcating solutions are spatially nonhomogeneous and orbitally asymptotically stable.

Abstract

The diffusive Holling-Tanner predator-prey model with no-flux boundary conditions and nonlocal prey competition is considered in this paper. We show the existence of spatial nonhomogeneous periodic solutions, which is induced by nonlocal prey competition. In particular, the constant positive steady state can lose the stability through Hopf bifurcation when the given parameter passes through some critical values, and the bifurcating periodic solutions near such values can be spatially nonhomogeneous and orbitally asymptotically stable. This phenomenon is different from that in models without nonlocal effect.