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LYAPUNOV EXPONENTS OF THE KURAMOTO–SIVASHINSKY PDE

Part of: Infinite-dimensional dissipative dynamical systems

Published online by Cambridge University Press:  15 July 2019

RUSSELL A. EDSON Open the ORCID record for RUSSELL A. EDSON [Opens in a new window] ,
J. E. BUNDER Open the ORCID record for J. E. BUNDER [Opens in a new window] ,
TRENT W. MATTNER Open the ORCID record for TRENT W. MATTNER [Opens in a new window]  and
A. J. ROBERTS Open the ORCID record for A. J. ROBERTS [Opens in a new window]
RUSSELL A. EDSON
Affiliation:
School of Mathematical Sciences, University of Adelaide, South Australia, Australia email russell.edson@adelaide.edu.au, judith.bunder@adelaide.edu.au, trent.mattner@adelaide.edu.au, anthony.roberts@adelaide.edu.au
J. E. BUNDER*
Affiliation:
School of Mathematical Sciences, University of Adelaide, South Australia, Australia email russell.edson@adelaide.edu.au, judith.bunder@adelaide.edu.au, trent.mattner@adelaide.edu.au, anthony.roberts@adelaide.edu.au
TRENT W. MATTNER
Affiliation:
School of Mathematical Sciences, University of Adelaide, South Australia, Australia email russell.edson@adelaide.edu.au, judith.bunder@adelaide.edu.au, trent.mattner@adelaide.edu.au, anthony.roberts@adelaide.edu.au
A. J. ROBERTS
Affiliation:
School of Mathematical Sciences, University of Adelaide, South Australia, Australia email russell.edson@adelaide.edu.au, judith.bunder@adelaide.edu.au, trent.mattner@adelaide.edu.au, anthony.roberts@adelaide.edu.au
*
✉judith.bunder@adelaide.edu.au
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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 one-dimensional turbulence.

Keywords

Lyapunov exponentsdynamical systems

MSC classification

Primary: 37L30: Attractors and their dimensions, Lyapunov exponents
Type
Research Article
Information
The ANZIAM Journal , Volume 61 , Issue 3 , July 2019 , pp. 270 - 285
Copyright
© 2019 Australian Mathematical Society 

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