Controlling Hamiltonian Chaos

Ying-Cheng Lai, Mingzhou Ding, Celso Grebogi

Research output: Contribution to journalArticle

121 Citations (Scopus)

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
Pages (from-to)86-92
Number of pages7
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume47
Issue number1
Publication statusPublished - Jan 1993

Keywords

  • Markov-tree model
  • systems
  • transport

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