Controlling Hamiltonian chaos

Ying Cheng Lai, Mingzhou Ding, Celso Grebogi

Research output: Contribution to journalArticle

120 Scopus citations

Abstract

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.

Original languageEnglish (US)
Pages (from-to)86-92
Number of pages7
JournalPhysical Review E
Volume47
Issue number1
DOIs
StatePublished - Jan 1 1993
Externally publishedYes

ASJC Scopus subject areas

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

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