# Lyapunov exponents of the Kuramoto-Sivashinsky PDE

## TL;DR

This paper analyzes how the chaotic dynamics of the Kuramoto-Sivashinsky PDE evolve with domain size by computing Lyapunov spectra, revealing insights into turbulence transition.

## Contribution

It provides the first comprehensive calculation of Lyapunov exponents across various domain sizes for the Kuramoto-Sivashinsky PDE, enhancing understanding of its chaotic behavior.

## Key findings

- Lyapunov spectra vary significantly with domain size.
- Transition to turbulence correlates with changes in Lyapunov exponents.
- Kaplan-Yorke dimension increases with domain size.

## 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.

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Source: https://tomesphere.com/paper/1902.09651