Extensive Chaos in the Nikolaevskii Model

Details Extensive Chaos in the Nikolaevskii Model Extensive Chaos in the Nikolaevskii Model

2000-02-08

arxiv.org/abs/cond-mat/0002118v1

Physics

Condensed Matter

4 pages (including 5 figures) LaTeX file. Submitted to Phys. Rev. Lett

Scientific paper

10.1103/PhysRevE.62.R17

We carry out a systematic study of a novel type of chaos at onset ("soft-mode turbulence") based on numerical integration of the simplest one dimensional model. The chaos is characterized by a smooth interplay of different spatial scales, with defect generation being unimportant. The Lyapunov exponents are calculated for several system sizes for fixed values of the control parameter $\epsilon$. The Lyapunov dimension and the Kolmogorov-Sinai entropy are calculated and both shown to exhibit extensive and microextensive scaling. The distribution functional is shown to satisfy Gaussian statistics at small wavenumbers and small frequency.

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