An analytical approach to initiation of propagating fronts

We consider the problem of initiation of a propagating wave in a one-dimensional excitable fibre. In the Zeldovich-Frank-Kamenetsky equation, a.k.a. Nagumo equation, the key role is played by the "critical nucleus'' solution whose stable manifold is the threshold surface separating initial conditions leading to initiation of propagation and to decay. Approximation of this manifold by its tangent linear space yields an analytical criterion of initiation which is in a good agreement with direct numerical simulations.