Hopf Bifurcation in a Reaction–Diffusion–Advection Population Model with Distributed Delay

Abstract

The existence, direction and stability of Hopf bifurcating periodic orbits near the positive spatially nonhomogeneous steady state of a reaction–diffusion–advection model with distributed delay and Dirichlet boundary condition are considered in this paper. By analyzing the characteristic equation and taking the bound of time delay as the bifurcation parameter, we show that Hopf bifurcation will occur when the shape parameter [Formula: see text], and the positive steady state is always stable when [Formula: see text]. The properties of Hopf bifurcations are then obtained by center manifold reduction and norm form methods. The effects of the distributed delay, shape parameter and advection on Hopf bifurcation values are also investigated. Finally, numerical simulations illustrate the effectiveness of the theoretical results.