An analytical approach to initiation of propagating fronts

I. Idris, V. N. Biktashev,

Submitted to PRL: 2008/09/01. Accepted: 2008/11/07.

We consider the problem of initiation of a propagating wave in a one-dimensional bistable or excitable fiber. In the Zeldovich-Frank-Kamenetsky equation, a.k.a. Nagumo equation and Schlögl model, 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.