Eckhaus and zigzag instability in a chemotaxis model of multiple sclerosis
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 concen...
| Main Authors: | , , , , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Accademia Peloritana dei Pericolanti
2018-11-01
|
| Series: | Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| Online Access: |
http://dx.doi.org/10.1478/AAPP.96S3A9
|
| _version_ | 1828485115215347712 |
|---|---|
| author | Eleonora Bilotta Francesco Gargano Valeria Giunta Maria Carmela Lombardo Pietro Pantano Paolo Falsaperla |
| author_facet | Eleonora Bilotta Francesco Gargano Valeria Giunta Maria Carmela Lombardo Pietro Pantano Paolo Falsaperla |
| author_sort | Eleonora Bilotta |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-12-11T09:07:16Z |
| format | Article |
| id | doaj.art-f4cf3a36f5164ed696ec89a2bac9e944 |
| institution | Directory Open Access Journal |
| issn | 0365-0359 1825-1242 |
| language | English |
| last_indexed | 2024-12-11T09:07:16Z |
| publishDate | 2018-11-01 |
| publisher | Accademia Peloritana dei Pericolanti |
| record_format | Article |
| series | Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| spelling | doaj.art-f4cf3a36f5164ed696ec89a2bac9e9442022-12-22T01:13:36ZengAccademia Peloritana dei PericolantiAtti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali0365-03591825-12422018-11-0196S3A910.1478/AAPP.96S3A9AAPP.96S3A9Eckhaus and zigzag instability in a chemotaxis model of multiple sclerosisEleonora BilottaFrancesco GarganoValeria GiuntaMaria Carmela LombardoPietro PantanoPaolo FalsaperlaWe 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. http://dx.doi.org/10.1478/AAPP.96S3A9 |
| spellingShingle | Eleonora Bilotta Francesco Gargano Valeria Giunta Maria Carmela Lombardo Pietro Pantano Paolo Falsaperla Eckhaus and zigzag instability in a chemotaxis model of multiple sclerosis Atti della Accademia Peloritana dei Pericolanti : Classe di Scienze Fisiche, Matematiche e Naturali |
| title | Eckhaus and zigzag instability in a chemotaxis model of multiple sclerosis |
| title_full | Eckhaus and zigzag instability in a chemotaxis model of multiple sclerosis |
| title_fullStr | Eckhaus and zigzag instability in a chemotaxis model of multiple sclerosis |
| title_full_unstemmed | Eckhaus and zigzag instability in a chemotaxis model of multiple sclerosis |
| title_short | Eckhaus and zigzag instability in a chemotaxis model of multiple sclerosis |
| title_sort | eckhaus and zigzag instability in a chemotaxis model of multiple sclerosis |
| url |
http://dx.doi.org/10.1478/AAPP.96S3A9
|
| work_keys_str_mv | AT eleonorabilotta eckhausandzigzaginstabilityinachemotaxismodelofmultiplesclerosis AT francescogargano eckhausandzigzaginstabilityinachemotaxismodelofmultiplesclerosis AT valeriagiunta eckhausandzigzaginstabilityinachemotaxismodelofmultiplesclerosis AT mariacarmelalombardo eckhausandzigzaginstabilityinachemotaxismodelofmultiplesclerosis AT pietropantano eckhausandzigzaginstabilityinachemotaxismodelofmultiplesclerosis AT paolofalsaperla eckhausandzigzaginstabilityinachemotaxismodelofmultiplesclerosis |