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Type: Journal article
Title: Lyapunov exponents of the Kuramoto-Sivashinksy PDE
Author: Edson, R.A.
Bunder, J.E.
Mattner, T.W.
Roberts, A.J.
Citation: Australia and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal, 2019; 61(3):270-285
Publisher: Cambridge University Press; Australian Mathematical Society
Issue Date: 2019
ISSN: 1446-1811
Statement of
Russell A. Edson, J.E. Bunder, Trent W. Mattner and A.J. Roberts
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 one-dimensional turbulence.
Keywords: Lyapunov exponents; dynamical systems
Rights: © Australian Mathematical Society 2019
DOI: 10.1017/S1446181119000105
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Mathematical Sciences publications

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