On stable nonconstant stationary solutions and mesoscopic patterns for FitzHugh-Nagumo equations in higher dimensions

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32 Citations (Scopus)

Abstract

FitzHugh-Nagumo equation has been studied extensively in the field of mathematical biology. It has the mechanism of "lateral inhibition" which seems to play a big role in the pattern formation of plankton distribution. We consider FitzHugh-Nagumo equation in high dimension and show the existence of stable nonconstant stationary solutions which have fine structures on a mesoscopic scale. We construct spatially periodic stationary solutions. Moreover, we compute the singular limit energy, which suggests that the transition from planar structure to droplet pattern can occur when parameters change.

Original languageEnglish
Pages (from-to)110-134
Number of pages25
JournalJournal of Differential Equations
Volume188
Issue number1
DOIs
Publication statusPublished - Feb 10 2003
Externally publishedYes

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FitzHugh-Nagumo Equations
Plankton
Stationary Solutions
Higher Dimensions
Mathematical Biology
Singular Limit
Fine Structure
Pattern Formation
Droplet
Lateral
Energy

Keywords

  • Fine structures
  • Mesoscopic scale
  • Pattern formation
  • Young's measure

ASJC Scopus subject areas

  • Analysis

Cite this

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AB - FitzHugh-Nagumo equation has been studied extensively in the field of mathematical biology. It has the mechanism of "lateral inhibition" which seems to play a big role in the pattern formation of plankton distribution. We consider FitzHugh-Nagumo equation in high dimension and show the existence of stable nonconstant stationary solutions which have fine structures on a mesoscopic scale. We construct spatially periodic stationary solutions. Moreover, we compute the singular limit energy, which suggests that the transition from planar structure to droplet pattern can occur when parameters change.

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