We construct square and target patterns solutions of the FitzHugh–Nagumo reaction–diffusion system on planar bounded domains. We study the existence and stability of stationary square and super-square patterns by performing a close to equilibrium asymptotic weakly nonlinear expansion: the emergence of these patterns is shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue without resonance. The system is also shown to support the formation of axisymmetric target patterns whose amplitude equation is derived close to the bifurcation threshold. We present several numerical simulations validating the theoretical results.

Gambino G., Lombardo M.C., Rubino G., & Sammartino M. (2019). Pattern selection in the 2D FitzHugh–Nagumo model. RICERCHE DI MATEMATICA, 68(2), 535-549 [10.1007/s11587-018-0424-6].

Pattern selection in the 2D FitzHugh–Nagumo model

Gambino G.
;
Lombardo M. C.;Rubino G.;Sammartino M.
2019

Abstract

We construct square and target patterns solutions of the FitzHugh–Nagumo reaction–diffusion system on planar bounded domains. We study the existence and stability of stationary square and super-square patterns by performing a close to equilibrium asymptotic weakly nonlinear expansion: the emergence of these patterns is shown to occur when the bifurcation takes place through a multiplicity-two eigenvalue without resonance. The system is also shown to support the formation of axisymmetric target patterns whose amplitude equation is derived close to the bifurcation threshold. We present several numerical simulations validating the theoretical results.
http://link.springer.com/journal/11587
Gambino G., Lombardo M.C., Rubino G., & Sammartino M. (2019). Pattern selection in the 2D FitzHugh–Nagumo model. RICERCHE DI MATEMATICA, 68(2), 535-549 [10.1007/s11587-018-0424-6].
File in questo prodotto:
File Dimensione Formato  
Gambino2018_Article_PatternSelectionInThe2DFitzHug.pdf

non disponibili

Tipologia: Versione Editoriale
Dimensione 2.25 MB
Formato Adobe PDF
2.25 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
Gambino2019_Article_PatternSelectionInThe2DFitzHug.pdf

non disponibili

Tipologia: Versione Editoriale
Dimensione 2.09 MB
Formato Adobe PDF
2.09 MB Adobe PDF   Visualizza/Apri   Richiedi una copia
2018_FN_selection_Lombardo.pdf

accesso aperto

Tipologia: Pre-print
Dimensione 1.88 MB
Formato Adobe PDF
1.88 MB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/10447/327139
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 16
  • ???jsp.display-item.citation.isi??? 15
social impact