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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Grégory Faye, Matt Holzer, Bifurcation to locked fronts in two component reaction–diffusion systems. Ann. Inst. H. Poincaré Anal. Non Linéaire 36 (2019), no. 2, pp. 545–584DOI 10.1016/J.ANIHPC.2018.08.001