Wavy fronts and speed bifurcation in excitable systems with cross diffusion.

A bifurcation of excitation fronts induced by cross diffusion in two-component bistable reaction-diffusion systems of activator-inhibitor type is discovered. This bifurcation is similar to the nonequilibrium Ising-Bloch bifurcation. A different type of fronts, whose spatial profiles are characterized by oscillating tails, are associated with this bifurcation. These fronts are described using exact analytical solutions of piecewise linear reaction-diffusion equations.