An analytical approach to initiation of propagating fronts

Abstract

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.

4 pages, 2 figures, submitted to Phys Rev Letters

References in corpus (1)

• Critical fronts in initiation of excitation waves

Cited by in corpus (9)

• Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems
• Semi-analytical approach to criteria for ignition of excitation waves
• Alternative Stable Scroll Waves and Conversion of Autowave Turbulence
• Fast-slow asymptotic for semi-analytical ignition criteria in FitzHugh-Nagumo system
• Quantitative estimates of the threshold phenomena for propagation in reaction-diffusion equations
• Predicting critical ignition in slow-fast excitable models
• Stability of pattern formation in systems with dynamic source regions
• Strength-Duration Relationship in an Excitable Medium
• On the stability of kink-like and soliton-like solutions to the generalized convection-reaction-diffusion equation