SPEED DETERMINACY OF TRAVELING WAVES TO A STREAM-POPULATION MODEL WITH ALLEE EFFECT

In this paper, we investigate the speed determinacy (or selection mechanism) of traveling waves to a reaction-advection-diffusion stream-population model. We concentrate on how the spreading speed (the minimal wave speed) is impacted by the Allee effect in the model. Linear and nonlinear selection mechanisms for the minimal speed (or the spreading speed) are first defined, and the determinacy is further established by way of the upper and lower solutions method. It is found that the nonlinear determinacy is realized if there exists a lower solution with a faster decay. The results obtained are novel, and numerical simulations are carried out to illustrate our discovery.