JournalsaihpcVol. 36, No. 2pp. 545–584

Bifurcation to locked fronts in two component reaction–diffusion systems

  • Grégory Faye

    Institut de Mathématiques de Toulouse, UMR 5219, Université de Toulouse, UPS IMT, 31062 Toulouse Cedex 9, France
  • Matt Holzer

    Department of Mathematical Sciences, George Mason University, Fairfax, VA 22030, USA
Bifurcation to locked fronts in two component reaction–diffusion systems cover
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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.

Cite this article

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. 545–584

DOI 10.1016/J.ANIHPC.2018.08.001