Parity-breaking front bifurcation in bistable media: link between discrete and continuous versions

The effect of space-discretization in the onset of traveling fronts in symmetrically bistable media is studied. For the FitzHugh-Nagumo model stable standing and propagating front solutions coexist. In the continuum limit this region of coexistence shrinks to a (double-zero eigenvalue) point. The unfolding of this point severely restricts the possible scenarios for the transition from standing to propagating fronts, such that the route described here and the one reported in [Phys. Rev. E 64 (2001) 065203(R)] are the most typical scenarios.