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