Reconstruction of chaotic saddles by classification of unstable periodic orbits: Kuramoto-Sivashinsky equation

The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from...

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Bibliographic Details
Published in:Chaos (Woodbury, N.Y.) N.Y.), 2015-10, Vol.25 (10), p.103123-103123
Main Authors: Saiki, Yoshitaka, Yamada, Michio, Chian, Abraham C-L, Miranda, Rodrigo A, Rempel, Erico L
Format: Article
Language:English
Subjects:
Astrophysics
ATTRACTORS
BIFURCATION
Bifurcations
CHAOS THEORY
CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
CLASSIFICATION
DIAGRAMS
EQUATIONS
Nonlinear Dynamics
ORBITS
PERIODICITY
Physics
Reconstruction
Saddles
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Summary:The unstable periodic orbits (UPOs) embedded in a chaotic attractor after an attractor merging crisis (MC) are classified into three subsets, and employed to reconstruct chaotic saddles in the Kuramoto-Sivashinsky equation. It is shown that in the post-MC regime, the two chaotic saddles evolved from the two coexisting chaotic attractors before crisis can be reconstructed from the UPOs embedded in the pre-MC chaotic attractors. The reconstruction also involves the detection of the mediating UPO responsible for the crisis, and the UPOs created after crisis that fill the gap regions of the chaotic saddles. We show that the gap UPOs originate from saddle-node, period-doubling, and pitchfork bifurcations inside the periodic windows in the post-MC chaotic region of the bifurcation diagram. The chaotic attractor in the post-MC regime is found to be the closure of gap UPOs.
ISSN:1054-1500
1089-7682
DOI:10.1063/1.4933267