Analysis of a Reaction–Diffusion–Advection Model with Various Allee Effects

Abstract

This paper presents an extensive study of traveling wave solutions for a population model where the growth function incorporates the Allee effect. We are able to find closed form solutions for solitary waves that are kinks and pulses (bell type). Additionally, for every solution that we find, we show the corresponding phase portrait. Interestingly, we discover that, under certain conditions, standing waves of the bell and kink types exist too.

Keywords

• population model
• reaction–diffusion–advection equation
• Allee threshold
• phase plane analysis
• solitary waves