Escape Time Weighting of Unstable Stationary Solutions of Spatiotemporal Chaos

1999/03/17 by Scott M. Zoldi, Zoldi, Scott M.
Earth and Planetary Sciences · Mathematics · Medicine · Physics and Astronomy · #Aquatic and Environmental Studies #Chaotic Dynamics (nlin.CD) #Differential Equations and Numerical Methods #FOS: Physical sciences #Mathematical and Theoretical Epidemiology and Ecology Models #chao-dyn #nlin.CD

paper · pdf · doi:10.48550/arxiv.chao-dyn/9903020

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arxiv created 1999/03/17 · openalex publication_date 1999/03/17 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

By computing 254 unstable stationary solutions of the Kuramoto-Sivashinsky equation in the extensive chaos regime (Lyapunov fractal dimension D=8.8), we find that 30% satisfy the symmetry of the time-average pattern of the spatiotemporal chaos. Using a symmetry pruning of unstable stationary solutions, the escape-time weighting average converges to the time-average pattern of the chaotic attractor as O(1/N), where N is the total number of unstable stationary solutions and unstable periodic orbits in the average.

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