English

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}
}