Speed determinacy of traveling waves for a lattice stream-population model with Allee effect

Abstract

This paper investigates the speed selection mechanism for traveling wave fronts of a reaction-diffusion-advection lattice stream-population model with the Allee effect. First, the asymptotic behaviors of the traveling wave solutions are given. Then, sufficient conditions for the speed determinacy of the traveling wave are successfully obtained by constructing appropriate upper and lower solutions. We examine the model with the reaction term $ f (\psi) = \psi(1-\psi)(1+\rho\psi) $, with $ \rho $ being a nonnegative constant, as a specific example. We give a novel conjecture that there exists a critical value $ \rho_c > 1 $, such that the minimal wave speed is linearly selected if and only if $ \rho\leq\rho_c $. Finally, our speculation is verified by numerical calculations.

Keywords

• lattice stream-population model
• allee effect
• traveling waves
• speed selection