Higher-dimensional targeting

Eric Kostelich, Celso Grebogi, Edward Ott, James A. Yorke

Research output: Contribution to journalArticle

102 Scopus citations


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 1011 iterates without the use of the targeting procedure.

Original languageEnglish (US)
Pages (from-to)305-310
Number of pages6
JournalPhysical Review E
Issue number1
StatePublished - Jan 1 1993


ASJC Scopus subject areas

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

Cite this

Kostelich, E., Grebogi, C., Ott, E., & Yorke, J. A. (1993). Higher-dimensional targeting. Physical Review E, 47(1), 305-310. https://doi.org/10.1103/PhysRevE.47.305