Pushed and pulled fronts in a logistic Keller-Segel model with chemorepulsion

TL;DR

This paper investigates how chemorepulsion influences the spreading speeds of populations in a logistic Keller-Segel model, distinguishing between pulled and pushed fronts through advanced mathematical analysis.

Contribution

It introduces a rigorous analysis of the transition between pulled and pushed fronts in a chemorepulsion model using geometric singular perturbation theory.

Findings

Identification of a sharp boundary between pulled and pushed fronts.

Characterization of spreading speeds using mathematical techniques.

Connection to recent PDE studies on singular limits.

Abstract

We analyze spatial spreading in a population model with logistic growth and chemorepulsion. In a parameter range of short-range chemo-diffusion, we use geometric singular perturbation theory and functional-analytic farfield-core decompositions to identify spreading speeds with marginally stable front profiles. In particular, we identify a sharp boundary between between linearly determined, pulled propagation, and nonlinearly determined, pushed propagation, induced by the chemorepulsion. The results are motivated by recent work on singular limits in this regime using PDE methods.