Bifurcation analysis for a single population model with advection.

Abstract

In this paper, the dynamics of a single population model with a general growth function is investigated in an advective environment. We show the existence of a nonconstant positive steady state, and give sufficient conditions for the occurrence of a Hopf bifurcation at the positive steady state. Moreover, the theoretical results are applied to the diffusive Nicholson's blowflies and Mackey-Glass's models with advection and delay, respectively. We numerically show that the population density decreases as the increase of advection rate or death rate, and a delay-induced Hopf bifurcation is more likely to occur with small advection or low mortality rate.