Bifurcation to locked fronts in two component reaction–diffusion systems

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.