### 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 language | English |
---|---|

Pages (from-to) | 305-310 |

Number of pages | 6 |

Journal | Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 47 |

Issue number | 1 |

Publication status | Published - Jan 1993 |

### Keywords

- CHAOS
- ATTRACTORS

### Cite this

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*,

*47*(1), 305-310.

**HIGHER-DIMENSIONAL TARGETING.** / KOSTELICH, E J ; GREBOGI, C ; OTT, E ; YORKE, J A .

Research output: Contribution to journal › Article

*Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics*, vol. 47, no. 1, pp. 305-310.

}

TY - JOUR

T1 - HIGHER-DIMENSIONAL TARGETING

AU - KOSTELICH, E J

AU - GREBOGI, C

AU - OTT, E

AU - YORKE, J A

PY - 1993/1

Y1 - 1993/1

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 10(11) 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 10(11) iterates without the use of the targeting procedure.

KW - CHAOS

KW - ATTRACTORS

M3 - Article

VL - 47

SP - 305

EP - 310

JO - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 1

ER -