A topological proof of stability of N-front solutions of the FitzHugh-Nagumo equations

Shunsaku Nii

doi:10.1023/A:1021965920761

A topological proof of stability of N-front solutions of the FitzHugh-Nagumo equations

Shunsaku Nii

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

8 Citations (Scopus)

Abstract

Consideration is devoted to traveling N-front wave solutions of the FitzHugh-Nagumo equations of the bistable type. Especially, stability of the N-front wave is proven. In the proof, the eigenvalue problem for the N-front wave bifurcating from coexisting simple front and back waves is regarded as a bifurcation problem for projectivised eigenvalue equations, and a topological index is employed to detect eigenvalues.

Original language	English
Pages (from-to)	515-555
Number of pages	41
Journal	Journal of Dynamics and Differential Equations
Volume	11
Issue number	3
DOIs	https://doi.org/10.1023/A:1021965920761
Publication status	Published - Jan 1 1999
Externally published	Yes

All Science Journal Classification (ASJC) codes

Analysis

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10.1023/A:1021965920761

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abstract = "Consideration is devoted to traveling N-front wave solutions of the FitzHugh-Nagumo equations of the bistable type. Especially, stability of the N-front wave is proven. In the proof, the eigenvalue problem for the N-front wave bifurcating from coexisting simple front and back waves is regarded as a bifurcation problem for projectivised eigenvalue equations, and a topological index is employed to detect eigenvalues.",

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AB - Consideration is devoted to traveling N-front wave solutions of the FitzHugh-Nagumo equations of the bistable type. Especially, stability of the N-front wave is proven. In the proof, the eigenvalue problem for the N-front wave bifurcating from coexisting simple front and back waves is regarded as a bifurcation problem for projectivised eigenvalue equations, and a topological index is employed to detect eigenvalues.

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A topological proof of stability of N-front solutions of the FitzHugh-Nagumo equations

Abstract

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