Hopf bifurcation in a two-species reaction-diffusion-advection competitive model with nonlocal delay

Abstract

In this paper, we are concerned with a two-species reaction-diffusion-advection competitive model with nonlocal delay subject to the homogeneous Dirichlet boundary conditions. The existence of the spatially inhomogeneous steady state is studied by using the implicit function theorem. The stability of the inhomogeneous steady state and the associated Hopf bifurcation are investigated by analyzing a non-self-adjoint linear operator. Taking the time delay as the bifurcation parameter, we obtain the critical value of time delay for the Hopf bifurcation and the stability switch phenomenon.