Fisher waves in the strong noise limit.
We investigate the effects of a 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.
Hallatschek
Oskar
O
Max Planck Research Group for Biological Physics and Evolutionary Dynamics, Max Planck Institute for Dynamics & Self-Organization (MPIDS), Göttingen, Germany. ohallats@gmail.com
Korolev
K S
KS
D004058:Diffusion; D016014:Linear Models; D008962:Models, Theoretical; D011789:Quantum Theory; D013269:Stochastic Processes