Lyapunov exponents of the Kuramoto--Sivashinsky PDE

Authors

  • Russell A. Edson University of Adelaide
  • Judith E. Bunder University of Adelaide
  • Trent W. Mattner University of Adelaide
  • Anthony J. Roberts University of Adelaide

DOI:

https://doi.org/10.21914/anziamj.v61i0.13939

Keywords:

Lyapunov exponents, dynamical systems.

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. doi:10.1017/S1446181119000105

Author Biographies

Russell A. Edson, University of Adelaide

School of Mathematical Sciences, University of Adelaide, South Australia, Australia.

Judith E. Bunder, University of Adelaide

School of Mathematical Sciences, University of Adelaide, South Australia, Australia.

Trent W. Mattner, University of Adelaide

School of Mathematical Sciences, University of Adelaide, South Australia, Australia.

Anthony J. Roberts, University of Adelaide

School of Mathematical Sciences, University of Adelaide, South Australia, Australia.

Published

2019-09-08

Issue

Vol. 61 (2019)

Section

Articles for Printed Issues