Controlling Hamiltonian chaos
Journal Article
·
· Physical Review E; (United States)
- Laboratory for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States) Department of Biomedical Engineering, The Johns Hopkins University School of Medicine, Baltimore, Maryland 21205 (United States)
- Center for Complex Systems, Florida Atlantic University, Boca Raton, Florida 33431 (United States) Department of Mathematics, Florida Atlantic University, Boca Raton, Florida 33431 (United States)
- Laboratory for Plasma Research, University of Maryland, College Park, Maryland 20742 (United States) Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States) Department of Mathematics, University of Maryland, College Park, Maryland 20742 (United States)
The method for stabilizing an unstable periodic orbit in chaotic dynamical systems originally formulated by Ott, Grebogi, and Yorke (OGY) is not directly applicable to chaotic Hamiltonian systems. The reason is that an unstable periodic orbit in such systems often exhibits complex-conjugate eigenvalues at one or more of its orbit points. In this paper we extend the OGY stabilization method to control Hamiltonian chaos by incorporating the notion of stable and unstable directions at each periodic point. We also present an algorithm to calculate the stable and unstable directions. Other issues specific to the control of Hamiltonian chaos are also discussed.
- OSTI ID:
- 6832891
- Journal Information:
- Physical Review E; (United States), Journal Name: Physical Review E; (United States) Vol. 47:1; ISSN PLEEE8; ISSN 1063-651X
- Country of Publication:
- United States
- Language:
- English
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