Chaotic Behavior in Shell Models and Shell Maps
| Autor: | Fridolin Okkels, Julien Kockelkoren, Mogens H. Jensen |
|---|---|
| Rok vydání: | 1998 |
| Předmět: |
Physics
Hopf bifurcation Condensed Matter (cond-mat) Mathematical analysis SHELL model Chaotic FOS: Physical sciences Statistical and Nonlinear Physics Condensed Matter Lyapunov exponent Nonlinear Sciences - Chaotic Dynamics Nonlinear Sciences::Chaotic Dynamics symbols.namesake symbols Chaotic Dynamics (nlin.CD) Invariant (mathematics) Mathematical Physics |
| Zdroj: | Journal of Statistical Physics. 93:833-842 |
| ISSN: | 0022-4715 |
| DOI: | 10.1023/b:joss.0000033165.51531.8c |
| Popis: | We study the chaotic behavior of the ``GOY'' shell model by measuring the variation of the maximal Lyapunov exponent with the parameter $\epsilon$ which determines the nature of the second invariant (the generalized ``helicity'' invariant). After a Hopf bifurcation, we observe a critical point at $\epsilon_c \sim 0.38704$ above which the maximal Lyapunov exponent grows nearly linearly. For high values of $\epsilon$ the evolution becomes regular again which can be explained by a simple analytic argument. A model with few shells shows two transitions. To simplify the model substantially we introduce a shell map which exhibits similar properties as the``GOY'' model. Comment: 4 pages REVTex, 8 Postscript figures, submitted to J. Stat. Phys |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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