Pinned pulse solutions in a FitzHugh–Nagumo model with a bump-type heterogeneity

Peter van Heijster; Takashi Teramoto

doi:10.2969/aspm/08510137

Pinned pulse solutions in a FitzHugh–Nagumo model with a bump-type heterogeneity

Peter van Heijster^*
, Takashi Teramoto^*

^*Corresponding author for this work

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

2 Citations (Scopus)

Abstract

In this article, we use geometric singular perturbation techniques combined with an action functional approach to study pinned pulse solutions in a three-component FitzHugh–Nagumo model with a bump-type heterogeneity. We show that the model in the original activator-2 inhibitor framework only supports symmetric pinned pulse solutions that are located in the middle of the bump region. In contrast, asymmetric pinning is possible for parameters not in the activator-2 inhibitor framework.

Original language	English
Pages (from-to)	137-150
Number of pages	14
Journal	Advanced Studies in Pure Mathematics
Volume	85
DOIs	https://doi.org/10.2969/aspm/08510137
Publication status	Published - 2020

Keywords

defects
pinning
Reaction-diffusion equations
singular perturbations

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10.2969/aspm/08510137

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title = "Pinned pulse solutions in a FitzHugh–Nagumo model with a bump-type heterogeneity",

abstract = "In this article, we use geometric singular perturbation techniques combined with an action functional approach to study pinned pulse solutions in a three-component FitzHugh–Nagumo model with a bump-type heterogeneity. We show that the model in the original activator-2 inhibitor framework only supports symmetric pinned pulse solutions that are located in the middle of the bump region. In contrast, asymmetric pinning is possible for parameters not in the activator-2 inhibitor framework.",

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AU - van Heijster, Peter

AU - Teramoto, Takashi

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N2 - In this article, we use geometric singular perturbation techniques combined with an action functional approach to study pinned pulse solutions in a three-component FitzHugh–Nagumo model with a bump-type heterogeneity. We show that the model in the original activator-2 inhibitor framework only supports symmetric pinned pulse solutions that are located in the middle of the bump region. In contrast, asymmetric pinning is possible for parameters not in the activator-2 inhibitor framework.

AB - In this article, we use geometric singular perturbation techniques combined with an action functional approach to study pinned pulse solutions in a three-component FitzHugh–Nagumo model with a bump-type heterogeneity. We show that the model in the original activator-2 inhibitor framework only supports symmetric pinned pulse solutions that are located in the middle of the bump region. In contrast, asymmetric pinning is possible for parameters not in the activator-2 inhibitor framework.

KW - defects

KW - pinning

KW - Reaction-diffusion equations

KW - singular perturbations

U2 - 10.2969/aspm/08510137

DO - 10.2969/aspm/08510137

M3 - Article

AN - SCOPUS:85119643465

SN - 0920-1971

VL - 85

SP - 137

EP - 150

JO - Advanced Studies in Pure Mathematics

JF - Advanced Studies in Pure Mathematics

ER -

Pinned pulse solutions in a FitzHugh–Nagumo model with a bump-type heterogeneity

Abstract

Keywords

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