Initiation of excitation waves: An analytical approach

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 ldquocritical nucleusrdquo solution whose stable manifold is the threshold surface separating initial conditions leading to initiation of propagation and to decay. In ionic models of cardiac excitation fronts, the same role is played by the center-stable manifold of the ldquocriticalrdquo front solution. Approximations of these manifolds by their tangent linear spaces yield analytical criteria of initiation. These criteria give a good quantitative approximation for simplified models and a useful qualitatively correct answer for the ionic models.