Hopf bifurcation in a delayed reaction-diffusion-advection population model

TL;DR

This paper studies how time delay influences stability and oscillatory behavior in a reaction-diffusion-advection population model, revealing that delay can induce Hopf bifurcation and oscillations.

Contribution

It provides a detailed analysis of Hopf bifurcation caused by time delay in a reaction-diffusion-advection model, highlighting the conditions for stability and oscillations.

Findings

Time delay can destabilize spatially nonhomogeneous steady states.

The model exhibits oscillatory patterns through Hopf bifurcation.

Stability depends on the principal eigenvalue of an elliptic operator.

Abstract

In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator. Our result implies that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction-diffusion-advection model, and the model can exhibit oscillatory pattern through Hopf bifurcation.