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2014 | OriginalPaper | Buchkapitel

2. Traveling Waves in One-Dimensional Excitable Media

verfasst von : Paul C. Bressloff

Erschienen in: Waves in Neural Media

Verlag: Springer New York

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Abstract

Chapter 2 covers the classical problem of waves in one-dimensional excitable media, as exemplified by the FitzHugh–Nagumo model of action potential propagation along an axon. Standard methods for analyzing front and pulse solutions of PDEs are described, including phase-plane analysis, singular perturbation methods and slow–fast analysis, and Evans functions for wave stability. In addition, the problem of wave propagation failure in myelinated axons is considered, where an averaging method is used to determine the effects of spatial discreteness on wave speed. This method is later used to analyze wave propagation failure in inhomogeneous neural fields. Finally, stochastic traveling waves are considered, where formal perturbation methods are used to show how to separate out fast fluctuations of the wave profile from the slow diffusive-like wandering of the wave.

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Metadaten
Titel
Traveling Waves in One-Dimensional Excitable Media
verfasst von
Paul C. Bressloff
Copyright-Jahr
2014
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-8866-8_2