Stabilizing chaotic-scattering trajectories using control

Ying-Cheng Lai, Tams Tél, Celso Grebogi

Research output: Contribution to journalArticle

56 Citations (Scopus)

Abstract

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 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.

Original languageEnglish (US)
Pages (from-to)709-717
Number of pages9
JournalPhysical Review E
Volume48
Issue number2
DOIs
StatePublished - 1993
Externally publishedYes

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trajectory control
Scattering
Trajectory
Periodic Orbits
Time-average
orbits
scattering
Unstable
Chaotic Dynamical Systems
Particle Trajectory
particle trajectories
Exponential Decay
Decay Rate
dynamical systems
decay rates
Hamiltonian Systems
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ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Stabilizing chaotic-scattering trajectories using control. / Lai, Ying-Cheng; Tél, Tams; Grebogi, Celso.

In: Physical Review E, Vol. 48, No. 2, 1993, p. 709-717.

Research output: Contribution to journalArticle

Lai, Ying-Cheng ; Tél, Tams ; Grebogi, Celso. / Stabilizing chaotic-scattering trajectories using control. In: Physical Review E. 1993 ; Vol. 48, No. 2. pp. 709-717.
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