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Title: 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 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.
Authors:
 [1] ;  [2] ;  [3] ;  [4] ;  [5] ;  [6] ;  [7] ;  [8] ;  [9]
  1. Graduate School of Commerce and Management, Hitotsubashi University, Tokyo 186-8601 (Japan)
  2. Research Institute for Mathematical Sciences (RIMS), Kyoto University, Kyoto 606-8502 (Japan)
  3. Paris Observatory, LESIA, CNRS, 92195 Meudon (France)
  4. (INPE), P.O. Box 515, São José dos Campos, São Paulo 12227-010 (Brazil)
  5. (ITA) and World Institute for Space Environment Research (WISER), São José dos Campos, São Paulo 12228-900 (Brazil)
  6. (Australia)
  7. (United States)
  8. Faculty UnB-Gama, and Plasma Physics Laboratory, Institute of Physics, University of Brasília (UnB), Brasília DF 70910-900 (Brazil)
  9. Institute of Aeronautical Technology (ITA) and World Institute for Space Environment Research (WISER), São José dos Campos, São Paulo 12228-900 (Brazil)
Publication Date:
OSTI Identifier:
22482287
Resource Type:
Journal Article
Resource Relation:
Journal Name: Chaos (Woodbury, N. Y.); Journal Volume: 25; Journal Issue: 10; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ATTRACTORS; BIFURCATION; CHAOS THEORY; CLASSIFICATION; DIAGRAMS; EQUATIONS; ORBITS; PERIODICITY