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arXiv · 1902.09651

Lyapunov exponents of the Kuramoto-Sivashinsky PDE

Russell A. Edson·J. E. Bunder·Trent W. Mattner·A. J. Roberts
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Abstract

The Kuramoto-Sivashinsky equation is a prototypical chaotic nonlinear partial differential equation (PDE) in which the size of the spatial domain plays the role of a bifurcation parameter. We investigate the changing dynamics of the Kuramoto-Sivashinsky PDE by calculating the Lyapunov spectra over a large range of domain sizes. Our comprehensive computation and analysis of the Lyapunov exponents and the associated Kaplan-Yorke dimension provides new insights into the chaotic dynamics of the Kuramoto-Sivashinsky PDE, and the transition to its 1D turbulence.

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BibTeXRIS

Russell A. Edson, J. E. Bunder, Trent W. Mattner, A. J. Roberts. 2019-02-25. Lyapunov exponents of the Kuramoto-Sivashinsky PDE. https://arxiv.org/abs/1902.09651

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