Chaotic Behavior in Shell Models and Shell Maps

Details Chaotic Behavior in Shell Models and Shell Maps Chaotic Behavior in Shell Models and Shell Maps

1998-01-20

arxiv.org/abs/chao-dyn/9801029v1

Physics

Condensed Matter

4 pages REVTex, 8 Postscript figures, submitted to J. Stat. Phys

Scientific paper

10.1023/B:JOSS.0000033165.51531.

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.

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