Advanced Studies in Pure Mathematics

Some recent progress on standing waves of FitzHugh–Nagumo system

Chao-Nien Chen and Hung-Jen Tsai

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Abstract

The FitzHugh–Nagumo system is a well-known reaction-diffusion model for exhibiting self-organized patterns. Besides regular patterns found in a neighborhood of Turing's instability, localized structures are also observed in experiment and numerical simulation. In particular, fronts and pulses are the most well-known localized structures in reaction-diffusion systems. This article is aimed at some recent results on the variational approach for studying standing waves of FitzHugh–Nagumo system.

Article information

Source
Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 63-75

Dates
Received: 11 May 2012
Revised: 21 February 2013
First available in Project Euclid: 30 October 2018

Permanent link to this document
https://projecteuclid.org/ euclid.aspm/1540934203

Digital Object Identifier
doi:10.2969/aspm/06410063

Mathematical Reviews number (MathSciNet)
MR3381192

Zentralblatt MATH identifier
1336.35197

Subjects
Primary: 34C37: Homoclinic and heteroclinic solutions 35J50: Variational methods for elliptic systems 35K57: Reaction-diffusion equations

Keywords
FitzHugh Nagumo system standing wave pattern variational method

Citation

Chen, Chao-Nien; Tsai, Hung-Jen. Some recent progress on standing waves of FitzHugh–Nagumo system. Nonlinear Dynamics in Partial Differential Equations, 63--75, Mathematical Society of Japan, Tokyo, Japan, 2015. doi:10.2969/aspm/06410063. https://projecteuclid.org/euclid.aspm/1540934203


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