# Bifurcation to locked fronts in two component reaction-diffusion systems

## TL;DR

This paper investigates bifurcations to locked fronts in two-component reaction-diffusion systems, constructing traveling solutions and analyzing how wave speeds depend on diffusion parameters, revealing complex bifurcation behaviors.

## Contribution

It introduces a variation of Lin's method to construct traveling fronts and characterizes the bifurcation to locked fronts, including wave speed expansions and bifurcation nature.

## Key findings

- Existence of bifurcation to locked fronts where both components invade at the same speed.
- Wave speed expansions as a function of diffusion constant.
- Numerical simulations show non-continuous dependence of spreading speed on diffusion coefficient.

## 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.