Subbasins, portals, and mazes: Transients in high dimensions☆

Abstract Transients in spatially-extended systems can be so long that the asymptotic invariant measure, or attractor, is irrelevant to the observed behavior. Even if the dynamics admits no local information production, a transient can appear quite complex spatially or temporally unpredictable. In such situations, the observed complexity depends on the basin structure in a high-dimensional state space. Statistical methods are used to elucidate the geometry of two broad classes of transient behavior: stationary and nonstationary.