Higher-dimensional targeting

Eric Kostelich, Celso Grebogi, Edward Ott, James 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 1011 iterates without the use of the targeting procedure.

Original languageEnglish (US)
Pages (from-to)305-310
Number of pages6
JournalPhysical Review E
Volume47
Issue number1
DOIs
StatePublished - 1993

Fingerprint

Iterate
High-dimensional
Chaotic Attractor
Target
Attractor
Mechanical Systems
Lyapunov Exponent
Control Parameter
Lyapunov
Initial conditions
Perturbation
exponents
perturbation

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear 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

Higher-dimensional targeting. / Kostelich, Eric; Grebogi, Celso; Ott, Edward; Yorke, James A.

In: Physical Review E, Vol. 47, No. 1, 1993, p. 305-310.

Research output: Contribution to journalArticle

Kostelich, E, Grebogi, C, Ott, E & Yorke, JA 1993, 'Higher-dimensional targeting', Physical Review E, vol. 47, no. 1, pp. 305-310. https://doi.org/10.1103/PhysRevE.47.305
Kostelich, Eric ; Grebogi, Celso ; Ott, Edward ; Yorke, James A. / Higher-dimensional targeting. In: Physical Review E. 1993 ; Vol. 47, No. 1. pp. 305-310.
@article{30d74e92b5a24c9eb75821a4717e2806,
title = "Higher-dimensional targeting",
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 1011 iterates without the use of the targeting procedure.",
author = "Eric Kostelich and Celso Grebogi and Edward Ott and Yorke, {James A.}",
year = "1993",
doi = "10.1103/PhysRevE.47.305",
language = "English (US)",
volume = "47",
pages = "305--310",
journal = "Physical Review E - Statistical, Nonlinear, and Soft Matter Physics",
issn = "1539-3755",
publisher = "American Physical Society",
number = "1",

}

TY - JOUR

T1 - Higher-dimensional targeting

AU - Kostelich, Eric

AU - Grebogi, Celso

AU - Ott, Edward

AU - Yorke, James A.

PY - 1993

Y1 - 1993

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=0001673690&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001673690&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.47.305

DO - 10.1103/PhysRevE.47.305

M3 - Article

VL - 47

SP - 305

EP - 310

JO - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

JF - Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

SN - 1539-3755

IS - 1

ER -