Stability and bifurcation in a reaction-diffusion-advection predator-prey model

TL;DR

This paper analyzes how diffusion and advection rates influence the stability and bifurcation behavior in a predator-prey model with reaction-diffusion-advection dynamics, revealing that advection can significantly affect Hopf bifurcations.

Contribution

It demonstrates the impact of large diffusion and advection rates on stability and bifurcation, highlighting the role of advection in Hopf bifurcation occurrence and parameters.

Findings

Positive steady state stability depends on diffusion and advection rates.

Large diffusion and advection can induce Hopf bifurcations.

Advection rate influences the occurrence and parameters of Hopf bifurcations.

Abstract

A reaction-diffusion-advection predator-prey model with Holling type-II predator functional response is considered. We show the stability/instability of the positive steady state and the existence of a Hopf bifurcation when the diffusion and advection rates are large. Moreover, we show that advection rate can affect not only the occurrence of Hopf bifurcations but also the values of Hopf bifurcations.