Bifurcation to locked fronts in two component reaction-diffusion systems
Pattern Formation and Solitons
2018-05-04 v2 Analysis of PDEs
Abstract
We study invasion fronts and spreading speeds in two component reaction-diffusion systems. Using a variation of Lin's method, we construct traveling front solutions and show the existence of a bifurcation to locked fronts where both components invade at the same speed. Expansions of the wave speed as a function of the diffusion constant of one species are obtained. The bifurcation can be sub or super-critical depending on whether the locked fronts exist for parameter values above or below the bifurcation value. Interestingly, in the sub-critical case numerical simulations reveal that the spreading speed of the PDE system does not depend continuously on the coefficient of diffusion.
Cite
@article{arxiv.1704.08604,
title = {Bifurcation to locked fronts in two component reaction-diffusion systems},
author = {Gregory Faye and Matt Holzer},
journal= {arXiv preprint arXiv:1704.08604},
year = {2018}
}