Persistence and Extinction of Population in Reaction-Diffusion-Advection Model with Weak Allee Effect Growth

Abstract

The dynamical behavior of a reaction-diffusion-advection model of a stream population with weak Allee effect type growth is studied. Under the open environment, it is shown that the persistence or extinction of population depends on the diffusion coefficient, advection rate, and type of boundary condition, and the existence of multiple positive steady states is proved for intermediate advection rate using bifurcation theory. On the other hand, for closed environment, the stream population always persists for all diffusion coefficients and advection rates.