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FRANCESCO GARGANO

Eckhaus and zigzag instability in a chemotaxis model of multiple sclerosis

  • Authors: Bilotta, Eleonora; Gargano, Francesco; Giunta, Valeria*; Lombardo, Maria Carmela; Pantano, Pietro; Sammartino, Marco
  • Publication year: 2018
  • Type: Articolo in rivista (Articolo in rivista)
  • Key words: 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)
  • OA Link: http://hdl.handle.net/10447/340307

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.