Advanced Studies in Pure Mathematics
- Adv. Stud. Pure Math.
- Nonlinear Dynamics in Partial Differential Equations, S. Ei, S. Kawashima, M. Kimura and T. Mizumachi, eds. (Tokyo: Mathematical Society of Japan, 2015), 63 - 75
Some recent progress on standing waves of FitzHugh–Nagumo system
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.
Received: 11 May 2012
Revised: 21 February 2013
First available in Project Euclid: 30 October 2018
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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