Traveling wave solutions for a density-suppressed motility model with strong Allee effect

Abstract

In this paper, we investigate a density-suppressed motility model with strong Allee effect. By leveraging existing results on asymptotic autonomous systems, along with Fredholm theory and the Banach fixed-point theorem, we establish the existence of bistable traveling wave solutions using a perturbation argument. This result holds when the density-suppressed sensitivity is relatively small. Finally, we validate our main results through numerical simulations and further discuss wave patterns and the sign of the wave speed as the density-suppressed sensitivity varies.