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Extensive Chaos in the Nikolaevskii Model

Hao-wen Xi·Raul Toral·J. D. Gunton·Michael I. Tribelsky
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Abstract

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 $ε$. 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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Hao-wen Xi, Raul Toral, J. D. Gunton, Michael I. Tribelsky. 2000-02-08. Extensive Chaos in the Nikolaevskii Model. https://doi.org/10.1103/physreve.62.r17

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