Ergodic theory of nonlinear waves in discrete and continuous excitable media
Veröffentlichungsdatum
2021-08-25
Autoren
Betreuer
Gutachter
Zusammenfassung
In this thesis, we analyze discrete and continuous models of excitable media with the intention to reveal similarities between both approaches in terms of wave propagation and interaction. While the discrete perspective is represented by the one-dimensional Greenberg-Hastings cellular automata (GHCA), as a continuous model we consider the $\theta$-equations which are basic partial differential equations (PDE) for pure phase dynamics. On the one hand, qualitatively, collision and annihilation of waves can be observed in both models in striking resemblance. However, on the other hand, it turns out that a quantitative comparison of discrete and continuous wave interactions is limited due to weak wave interactions in the PDE. Specifically, complexity considerations show that a direct comparison of discrete and continuous strong wave interactions is problematic.
Schlagwörter
dynamical systems
;
partial differential equations
;
cellular atomata
;
ergodic theory
;
complexity
;
nonlinear waves
;
excitable media
Institution
Dokumenttyp
Dissertation
Zweitveröffentlichung
Nein
Sprache
Englisch
Dateien![Vorschaubild]()
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Name
Dissertation_UlbrichDennis.pdf
Size
1,39 MB
Format
Adobe PDF
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