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In this paper, we investigate a delayed reaction-diffusion-advectionequation, which models the population dynamics in the advective heterogeneousenvironment. The existence of the nonconstant positive steady state andassociated Hopf bifurcation are obtained. A weighted inner product associatedwith the advection rate is introduced to compute the normal forms, which is themain difference between Hopf bifurcation for delayedreaction-diffusion-advection model and that for delayed reaction-diffusionmodel. Moreover, we find that the spatial scale and advection can affect Hopfbifurcation in the heterogenous environment.

Hopf bifurcation for a delayed diffusive logistic population model in the advective heterogeneous environment