Lyapunov exponents of the Kuramoto-Sivashinsky PDE
Russell A. Edson, J. E. Bunder, Trent W. Mattner, A. J. Roberts
TL;DR
This paper analyzes how the chaotic dynamics of the Kuramoto-Sivashinsky PDE evolve with domain size by computing Lyapunov spectra, revealing insights into turbulence transition.
Contribution
It provides the first comprehensive calculation of Lyapunov exponents across various domain sizes for the Kuramoto-Sivashinsky PDE, enhancing understanding of its chaotic behavior.
Findings
Lyapunov spectra vary significantly with domain size.
Transition to turbulence correlates with changes in Lyapunov exponents.
Kaplan-Yorke dimension increases with domain size.
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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Taxonomy
TopicsNonlinear Dynamics and Pattern Formation