Extensive Chaos in the Nikolaevskii Model

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 $\epsilon$. 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.

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

References in corpus (5)

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• Direct Transition to Spatiotemporal Chaos in Low Prandtl Number Fluids
• Defect-Mediated Stability: An Effective Hydrodynamic Theory of Spatio-Temporal Chaos
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Cited by in corpus (7)

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• Quantifying Spatiotemporal Chaos in Rayleigh-Bénard Convection
• Chemical turbulence equivalent to Nikolavskii turbulence
• Microextensive Chaos of a Spatially Extended System
• Critical exponents of Nikolaevskii turbulence
• Transition between chaotic and stochastic universality classes of kinetic roughening
• New scenario for transition to slow 3D turbulence