Speed and shape of population fronts with density-dependent diffusion
Populations and Evolution
2024-11-19 v2 Dynamical Systems
Abstract
We investigate travelling wave solutions in reaction-diffusion models of animal range expansion in the case that population diffusion is density-dependent. We find that the speed of the selected wave depends critically on the strength of diffusion at low density. For sufficiently large low-density diffusion, the wave propagates at a speed predicted by a simple linear analysis. For small or zero low-density diffusion, the linear analysis is not sufficient, but a variational approach yields exact or approximate expressions for the speed and shape of population fronts.
Keywords
Cite
@article{arxiv.2407.07915,
title = {Speed and shape of population fronts with density-dependent diffusion},
author = {Beth M. Stokes and Tim Rogers and Richard James},
journal= {arXiv preprint arXiv:2407.07915},
year = {2024}
}