HIGHER-DIMENSIONAL TARGETING

E J KOSTELICH, C GREBOGI, E OTT, J A YORKE

Research output: Contribution to journalArticle

101 Citations (Scopus)

Abstract

This paper describes a procedure to steer rapidly successive iterates of an initial condition on a chaotic attractor to a small target region about any prespecified point on the attractor using only small controlling perturbations. Such a procedure is called ''targeting.'' Previous work on targeting for chaotic attractors has been in the context of one- and two-dimensional maps. Here it is shown that targeting can also be done in higher-dimensional cases. The method is demonstrated with a mechanical system described by a four-dimensional mapping whose attractor has two positive Lyapunov exponents and a Lyapunov dimension of 2.8. The target is reached by making very small successive changes in a single control parameter. In one typical case, 35 iterates on average are required to reach a target region of diameter 10(-4), as compared to roughly 10(11) iterates without the use of the targeting procedure.

Original languageEnglish
Pages (from-to)305-310
Number of pages6
JournalPhysical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume47
Issue number1
Publication statusPublished - Jan 1993

Keywords

  • CHAOS
  • ATTRACTORS

Cite this