Analytical Approach to Initiation of Propagating Fronts

Abstract

We consider the problem of initiation of a propagating wave in a one-dimensional bistable or excitable fiber. In the Zeldovich-Frank-Kamenetskii equation, also known as the Nagumo equation and Schl\"ogl model, the key role is played by the ``critical nucleus'' solution whose stable manifold is the threshold surface separating initial conditions leading to the initiation of propagation and decay. An approximation of this manifold by its tangent linear space yields an analytical criterion of initiation which is in good agreement with direct numerical simulations.