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arXiv · chao-dyn/9801029

Chaotic Behavior in Shell Models and Shell Maps

Julien Kockelkoren·Fridolin Okkels·Mogens H. Jensen
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Abstract

We study the chaotic behavior of the ``GOY'' shell model by measuring the variation of the maximal Lyapunov exponent with the parameter $ε$ which determines the nature of the second invariant (the generalized ``helicity'' invariant). After a Hopf bifurcation, we observe a critical point at $ε_c \sim 0.38704$ above which the maximal Lyapunov exponent grows nearly linearly. For high values of $ε$ 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.

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Julien Kockelkoren, Fridolin Okkels, Mogens H. Jensen. 1998-01-20. Chaotic Behavior in Shell Models and Shell Maps. https://doi.org/10.1023/b%3Ajoss.0000033165.51531.8c

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