Eckhaus and zigzag instability in a chemotaxis model of multiple sclerosis

Maria Carmela Lombardo, Marco Maria Luigi Sammartino, Francesco Gargano, Eleonora Bilotta, Pietro Pantano, Valeria Giunta

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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.
Lingua originaleEnglish
Numero di pagine18
RivistaATTI DELLA ACCADEMIA PELORITANA DEI PERICOLANTI, CLASSE DI SCIENZE FISICHE MATEMATICHE E NATURALI
Volume96
Stato di pubblicazionePublished - 2018

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All Science Journal Classification (ASJC) codes

  • Computer Science(all)
  • Chemistry(all)
  • Mathematics(all)
  • Agricultural and Biological Sciences(all)
  • Physics and Astronomy(all)
  • History and Philosophy of Science
  • Earth and Planetary Sciences(all)

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