STATIONARY, DYNAMICAL, AND CHAOTIC STATES OF THE 2-DIMENSIONAL DAMPEDKURAMOTO-SIVASHINSKY EQUATION

The long-time behavior of the two-dimensional damped Kuramoto-Sivashin sky equation is studied numerically in the large-aspect-ratio limit. T he equation is shown to lead to three states depending on the magnitud e of a damping parameter alpha. At large, intermediate, and small valu es of alpha, the equation leads respectively to hexagonal, breathing h exagonal, and disordered states. The disordered phase is chaotic in bo th space and time, consistent with spatiotemporal chaos. The transitio ns between these states are examined using standard statistical measur es.