On the "traveling pulses" of the limit of the FitzHugh-Nagumo equation when ɛ→0
A solution (u(s), v(s)) of the differential system u = v, v = -cv-u(u-a)(1-u) + w, w = -(ɛ/c)(u-γw) with a, c, ɛ ∈ R such that (u(s), v(s)) → (0,0) when s → ± ∞ is a traveling pulse of the FitzHugh-Nagumo equation. The limit of this differential system when ɛ → 0 gives rise to the polynomial differe...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2023 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:281984 |
| Acceso en línea: | https://ddd.uab.cat/record/281984 https://dx.doi.org/urn:doi:10.1016/j.nonrwa.2023.103891 |
| Access Level: | acceso abierto |
| Palabra clave: | FitzHugh-Nagumo system Poincaré compactification Dynamics at infinity Traveling pulse |
| Sumario: | A solution (u(s), v(s)) of the differential system u = v, v = -cv-u(u-a)(1-u) + w, w = -(ɛ/c)(u-γw) with a, c, ɛ ∈ R such that (u(s), v(s)) → (0,0) when s → ± ∞ is a traveling pulse of the FitzHugh-Nagumo equation. The limit of this differential system when ɛ → 0 gives rise to the polynomial differential system u = v, v = -cv-u(u-a)(1-u) + w, where now a, c,w ∈ R. We give the complete description of its phase portraits in the Poincaré disc (i.e. in the compactification of R adding the circle S of the infinity) modulo topological equivalence. |
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