Lyapunov exponents of the Kuramoto-Sivashinsky PDE
Dynamical Systems
2019-02-27 v1 Chaotic Dynamics
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.
Keywords
Cite
@article{arxiv.1902.09651,
title = {Lyapunov exponents of the Kuramoto-Sivashinsky PDE},
author = {Russell A. Edson and J. E. Bunder and Trent W. Mattner and A. J. Roberts},
journal= {arXiv preprint arXiv:1902.09651},
year = {2019}
}