Fisher waves in the strong noise limit

Details Fisher waves in the strong noise limit Fisher waves in the strong noise limit

2009-05-07

arxiv.org/abs/0905.1083v2

Biology

Quantitative Biology

Populations and Evolution

4 pages, 2 figures, update

Scientific paper

We investigate the effects of strong number fluctuations on traveling waves in the Fisher-Kolmogorov reaction-diffusion system. Our findings are in stark contrast to the commonly used deterministic and weak-noise approximations. We compute the wave velocity in one and two spatial dimensions, for which we find a linear and a square-root dependence of the speed on the particle density. Instead of smooth sigmoidal wave profiles, we observe fronts composed of a few rugged kinks that diffuse, annihilate, and rarely branch; this dynamics leads to power-law tails in the distribution of the front sizes.

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