Eckhaus and zigzag instability in a chemotaxis model of multiple sclerosis

Autori

  • Eleonora Bilotta Università degli Studi della Calabria
  • Francesco Gargano Università degli Studi di Palermo
  • Valeria Giunta Università degli Studi di Palermo
  • Maria Carmela Lombardo Università degli Studi di Palermo
  • Pietro Pantano Università degli Studi della Calabria
  • Marco Sammartino Università degli Studi di Palermo

DOI:

https://doi.org/10.1478/AAPP.96S3A9

Abstract

We present a theoretical and numerical study of the bifurcations of the stationary patterns supported by a chemotactic model of Multiple Sclerosis (MS). We derive the normal forms of the dynamics which allows to predict the appearance and stabilization of the emerging branches describing the concentric patterns typical of Balo's sclerosis, a very aggressive variant of MS. Spatial modulation of the Turing-type structures through a zigzag instability is also addressed. The nonlinear stage of the Eckhaus and zigzag instability is investigated numerically: defect-mediated wavenumber adjustments are recovered and the time of occurrence of phase-slips is studied as the system parameters are varied.

Biografie autore

  • Eleonora Bilotta, Università degli Studi della Calabria
    Dipartimento di Fisica, Via Pietro Bucci, 87036 Rende (Cosenza)
  • Francesco Gargano, Università degli Studi di Palermo
    Dipartimento di Energia, Ingegneria dell’Informazione e Modelli Matematici, Viale delle Scienze Ed.9, 90128 Palermo
  • Valeria Giunta, Università degli Studi di Palermo
    Dipartimento di Matematica e Informatica, Via Archirafi 34, 90123 Palermo
  • Maria Carmela Lombardo, Università degli Studi di Palermo
    Dipartimento di Matematica e Informatica, Via Archirafi 34, 90123 Palermo
  • Pietro Pantano, Università degli Studi della Calabria
    Dipartimento di Fisica, Via Pietro Bucci, 87036 Rende (Cosenza)
  • Marco Sammartino, Università degli Studi di Palermo
    Dipartimento di Ingegneria Chimica, Gestionale, Informatica, Meccanica, Viale delle Scienze Ed. 8, 90128 Palermo
Trinacria

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Pubblicato

2018-11-30

Fascicolo

Vol 96, SUPPL NO 3 (2018): M.M.SE.OR.2017

Sezione

M.M.SE.OR. 2017 (Conference Proceedings)

Licenza

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