Multipeak solutions for the Neumann problem of an elliptic system of FitzHugh-Nagumo type

Edward Norman Dancer; Shusen Yan

doi:10.1112/S0024611504014947

Multipeak solutions for the Neumann problem of an elliptic system of FitzHugh-Nagumo type

Edward Norman Dancer, Shusen Yan

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

This parabolic system in one space dimension is a simplification of the original Hodgkin-Huxley nerve conduction equations. Here u denotes an activator and v acts as its inhibitor. This system has also been studied in many applied areas. The readers can find more references in for the background of the systems of FitzHugh--Nagumo type. Here we mention some early results on the systems of FitzHugh--Nagumo type, obtained by Klaasen and Troy, Klaasen and Mitidieri and DeFigueiredo and Mitidieri.

Original language	English
Pages (from-to)	209-244
Journal	Proceedings of the London Mathematical Society
Volume	90
Issue number	1
DOIs	https://doi.org/10.1112/S0024611504014947
Publication status	Published - 2005

Keywords

Ordinary Differential Equations, Difference Equations and Dynamical Systems

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https://hdl.handle.net/1959.11/3606

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abstract = "This parabolic system in one space dimension is a simplification of the original Hodgkin-Huxley nerve conduction equations. Here u denotes an activator and v acts as its inhibitor. This system has also been studied in many applied areas. The readers can find more references in for the background of the systems of FitzHugh--Nagumo type. Here we mention some early results on the systems of FitzHugh--Nagumo type, obtained by Klaasen and Troy, Klaasen and Mitidieri and DeFigueiredo and Mitidieri.",

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author = "Dancer, \{Edward Norman\} and Shusen Yan",

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AU - Dancer, Edward Norman

AU - Yan, Shusen

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AB - This parabolic system in one space dimension is a simplification of the original Hodgkin-Huxley nerve conduction equations. Here u denotes an activator and v acts as its inhibitor. This system has also been studied in many applied areas. The readers can find more references in for the background of the systems of FitzHugh--Nagumo type. Here we mention some early results on the systems of FitzHugh--Nagumo type, obtained by Klaasen and Troy, Klaasen and Mitidieri and DeFigueiredo and Mitidieri.

KW - Ordinary Differential Equations, Difference Equations and Dynamical Systems

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DO - 10.1112/S0024611504014947

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EP - 244

JO - Proceedings of the London Mathematical Society

JF - Proceedings of the London Mathematical Society

IS - 1

ER -

Multipeak solutions for the Neumann problem of an elliptic system of FitzHugh-Nagumo type

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