Kuramoto-Sivashinsky Equation: Spatio-Temporal Chaos and Intermittencies for a Dynamical System

摘要

We survey some recent results on the finite-dimensional behavior of the Kuramoto-Sivashinsky equation. We outline how it is rigorously equivalent to a finite dimensional dynamical system on a finite ''inertial'' manifold; a geometric approach to the construction of such a manifold is given. We give some examples of computational simulations supporting the evidence for a low-dimensional vector field which rules the bifurcations of the inertial manifold. 45 refs., 21 figs. (ERA citation 12:010655)