  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.
