Stationary, dynamical, and chaotic states of the two-dimensional damped Kuramoto-Sivashinsky equation

The long-time behavior of the two-dimensional damped Kuramoto-Sivashinsky equation is studied numerically in the large-aspect-ratio limit. The equation is shown to lead to three states depending on the magnitude of a damping parameter α. At large, intermediate, and small values of α, the equation leads respectively to hexagonal, breathing hexagonal, and disordered states. The disordered phase is chaotic in both space and time, consistent with spatiotemporal chaos. The transitions between these states are examined using standard statistical measures.