The FitzHugh-Nagumo system on undulated cylinders: spontaneous symmetrization and effective system
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866913802163847168 |
|---|---|
| author | Karali, Georgia Tzirakis, Konstantinos Sigal, Israel Michael |
| author_facet | Karali, Georgia Tzirakis, Konstantinos Sigal, Israel Michael |
| contents | We consider the FitzHugh-Nagumo system on undulated cylindrical surfaces modeling nerve axons. We show that for sufficiently small radii and for initial conditions close to radially symmetrical ones, (i) the solutions converge to their radial averages, and (ii) the latter averages can be approximated by solutions of a 1+1 dimensional ('radial') system (the effective system) involving the surface radius function in its coefficients. This perhaps explains why solutions of the original 1+1 dimensional FitzHugh-Nagumo system agree so well with experimental data on electrical impulse propagation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_07003 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The FitzHugh-Nagumo system on undulated cylinders: spontaneous symmetrization and effective system Karali, Georgia Tzirakis, Konstantinos Sigal, Israel Michael Analysis of PDEs 35C07, 37N25, 35Q92, 35B07, 35K57, 46N60, 92-08, 92-10, 92C20, 35K91 We consider the FitzHugh-Nagumo system on undulated cylindrical surfaces modeling nerve axons. We show that for sufficiently small radii and for initial conditions close to radially symmetrical ones, (i) the solutions converge to their radial averages, and (ii) the latter averages can be approximated by solutions of a 1+1 dimensional ('radial') system (the effective system) involving the surface radius function in its coefficients. This perhaps explains why solutions of the original 1+1 dimensional FitzHugh-Nagumo system agree so well with experimental data on electrical impulse propagation. |
| title | The FitzHugh-Nagumo system on undulated cylinders: spontaneous symmetrization and effective system |
| topic | Analysis of PDEs 35C07, 37N25, 35Q92, 35B07, 35K57, 46N60, 92-08, 92-10, 92C20, 35K91 |
| url | https://arxiv.org/abs/2504.07003 |