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arXiv · 1704.08604

Bifurcation to locked fronts in two component reaction-diffusion systems

Gregory Faye·Matt Holzer
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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.

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Gregory Faye, Matt Holzer. 2017-04-27. Bifurcation to locked fronts in two component reaction-diffusion systems. https://arxiv.org/abs/1704.08604

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