Hopf Bifurcation in a reaction–diffusion–advection model with two nonlocal delayed density-dependent feedback terms

Abstract

We consider a reaction–diffusion–advection logistic model with two nonlocal delayed density-dependent terms and zero-Dirichlet boundary conditions. The existence of positive non-homogeneous steady states and the associated Hopf bifurcation are obtained. By taking the time delay τ as the bifurcation parameter, we find that the system may admit no stability switches, a single stability switch and multiple stability switches. Moreover, we investigate the influence of advection on the Hopf bifurcation and stability switches, and find that the critical values of τ at which a Hopf bifurcation occurs increase (decrease) as the advection rate α increases in a positive (negative) range, which implies that the advective effect has decelerated (accelerated) the generation of Hopf bifurcation to some extent if the advection rate α lies in a certain positive (negative) range.