Stabilizing chaotic-scattering trajectories using control

Ying Cheng Lai, Tams Tél, Celso Grebogi

Research output: Contribution to journalArticlepeer-review

59 Scopus citations


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
Issue number2
StatePublished - Jan 1 1993
Externally publishedYes

ASJC Scopus subject areas

  • Statistical and Nonlinear Physics
  • Statistics and Probability
  • Condensed Matter Physics


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