Propagation of Turing–Hopf fronts

We investigate the dynamics of fronts between Turing- and Hopf-type domains close to the respective co-dimension two bifurcation in terms of coupled amplitude equations. In particular, we derive a dominance rule for the velocity of these fronts and explain the recently observed phenomenon of a returning front by introducing the concept of a current of the local wave number. This current is induced by the presence of a front and leads to a slow change of the front velocity and of the domain solutions.