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arXiv · 2407.07915

Speed and shape of population fronts with density-dependent diffusion

Beth M. Stokes·Tim Rogers·Richard James
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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.

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Beth M. Stokes, Tim Rogers, Richard James. 2024-07-05. Speed and shape of population fronts with density-dependent diffusion. https://doi.org/10.1007/s11538-024-01381-2

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