Stabilizing chaotic-scattering trajectories using control

Journal Article · Sun Aug 01 04:00:00 EDT 1993 · Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States)

DOI:https://doi.org/10.1103/PhysRevE.48.709· OSTI ID:6027092

Lai, Y ^[1]; Tel, T ^[2]; Grebogi, C ^[3]

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1. 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)
2. Institute for Theoretical Physics, Eoetvoes University, Puskin, ulica 5-7, H-1088 Budapest (Hungary)
3. Laboratory for Plasma Research, Department of Mathematics, and Institute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742 (United States)

The method of stabilizing unstable periodic orbits in chaotic dynamical systems by Ott, Grebogi, and Yorke (OGY) is applied to control chaotic scattering in Hamiltonian systems. In particular, we consider the case of [ital nonhyperbolic] chaotic scattering, where there exist Kolmogorov-Arnold-Moser (KAM) surfaces in the scattering region. It is found that for short unstable periodic orbits not close to the KAM surfaces, both the probability that a particle can be controlled and the average time to achieve control are determined by the initial exponential decay rate of particles in the hyperbolic component. For periodic orbits near the KAM surfaces, due to the stickiness effect of the KAM surfaces on particle trajectories, the average time to achieve control can greatly exceed that determined by the hyperbolic component. The applicability of the OGY method to stabilize intermediate complexes of classical scattering systems is suggested.

• OSTI ID: 6027092
• Journal Information: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States), Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; (United States) Vol. 48:2; ISSN PLEEE8; ISSN 1063-651X
• Country of Publication: United States
• Language: English

Related Subjects

661300* -- Other Aspects of Physical Science-- (1992-)
71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
DECAY
HAMILTONIANS
MATHEMATICAL OPERATORS
ORBIT STABILITY
QUANTUM OPERATORS
SCATTERING
STABILITY
STOCHASTIC PROCESSES