Abstract
Chaotic pattern dynamics in many experimental systems show structured time averages. We suggest that simple universal boundary effects underly this phenomenon and exemplify them with the Kuramoto-Sivashinsky equation in a finite domain. As in the experiments, averaged patterns in the equation recover global symmetries locally broken in the chaotic field. Plateaus in the average pattern wave number as a function of the system size are observed and studied and the different behaviors at the central and boundary regions are discussed. Finally, the structure strength of average patterns is investigated as a function of system size.
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