Lyapunov exponents of the Kuramoto-Sivashinsky PDE

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.