The control of chaos: theory and applications

S  Boccaletti; C  Grebogi; Y C  Lai; H  Mancini; D  Maza; Ying-Cheng Lai

doi:10.1016/S0370-1573(99)00096-4

The control of chaos: theory and applications

S Boccaletti, C Grebogi, Y C Lai, H Mancini, D Maza, Ying-Cheng Lai

Physics

Research output: Contribution to journal › Article › peer-review

888 Citations (Scopus)

Abstract

Control of chaos refers to a process wherein a tiny perturbation is applied to a chaotic system, in order to realize a desirable (chaotic, periodic, or stationary) behavior. We review the major ideas involved in the control of chaos, and present in detail two methods: the Ott-Grebogi-Yorke (OGY) method and the adaptive method. We also discuss a series of relevant issues connected with chaos control, such as the targeting problem, i.e., how to bring a trajectory to a small neighborhood of a desired location in the chaotic attractor in both low and high dimensions, and point out applications for controlling fractal basin boundaries. In short, we describe procedures for stabilizing desired chaotic orbits embedded in a chaotic attractor and discuss the issues of communicating with chaos by controlling symbolic sequences and of synchronizing chaotic systems. Finally, we give a review of relevant experimental applications of these ideas and techniques. (C) 2000 Elsevier Science B.V. All rights reserved.

Original language	English
Pages (from-to)	103-197
Number of pages	95
Journal	Physics Reports
Volume	329
Issue number	3
Early online date	31 Mar 2000
DOIs	https://doi.org/10.1016/S0370-1573(99)00096-4
Publication status	Published - May 2000

Bibliographical note

The authors are grateful to F.T. Arecchi, E. Barreto, G. Basti, E. Bollt, A. Farini, R. Genesio, A. Giaquinta, S. Hayes, E. Kostelich, A.L. Perrone, F. Romeiras and T. Tél for many fruitful discussions. SB acknowledges financial support from the EEC Contract no. ERBFMBICT983466. CG was supported by DOE and by a joint Brasil-USA grant (CNPq/NSF-INT). YCL was supported by AFOSR under Grant No. F49620-98-1-0400 and by NSF under Grant No. PHY-9722156. HM and DM acknowledge financial support from Ministerio de Educacion y Ciencia (Grant N. PB95-0578) and Universidad de Navarra, Spain (PIUNA).

Keywords

unstable periodic-orbits
fractal basin boundaries
resonant parametric perturbations
time-delay autosynchronization
Belousov-Zhabotinsky Reaction
crisis-induced intermittency
high-dimensional chaos
dynamical-systems
strange attractors
adaptive recognition

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title = "The control of chaos: theory and applications",

abstract = "Control of chaos refers to a process wherein a tiny perturbation is applied to a chaotic system, in order to realize a desirable (chaotic, periodic, or stationary) behavior. We review the major ideas involved in the control of chaos, and present in detail two methods: the Ott-Grebogi-Yorke (OGY) method and the adaptive method. We also discuss a series of relevant issues connected with chaos control, such as the targeting problem, i.e., how to bring a trajectory to a small neighborhood of a desired location in the chaotic attractor in both low and high dimensions, and point out applications for controlling fractal basin boundaries. In short, we describe procedures for stabilizing desired chaotic orbits embedded in a chaotic attractor and discuss the issues of communicating with chaos by controlling symbolic sequences and of synchronizing chaotic systems. Finally, we give a review of relevant experimental applications of these ideas and techniques. (C) 2000 Elsevier Science B.V. All rights reserved.",

keywords = "unstable periodic-orbits, fractal basin boundaries, resonant parametric perturbations, time-delay autosynchronization, Belousov-Zhabotinsky Reaction, crisis-induced intermittency, high-dimensional chaos, dynamical-systems, strange attractors, adaptive recognition",

author = "S Boccaletti and C Grebogi and Lai, {Y C} and H Mancini and D Maza and Ying-Cheng Lai",

note = "The authors are grateful to F.T. Arecchi, E. Barreto, G. Basti, E. Bollt, A. Farini, R. Genesio, A. Giaquinta, S. Hayes, E. Kostelich, A.L. Perrone, F. Romeiras and T. T{\'e}l for many fruitful discussions. SB acknowledges financial support from the EEC Contract no. ERBFMBICT983466. CG was supported by DOE and by a joint Brasil-USA grant (CNPq/NSF-INT). YCL was supported by AFOSR under Grant No. F49620-98-1-0400 and by NSF under Grant No. PHY-9722156. HM and DM acknowledge financial support from Ministerio de Educacion y Ciencia (Grant N. PB95-0578) and Universidad de Navarra, Spain (PIUNA).",

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doi = "10.1016/S0370-1573(99)00096-4",

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T2 - theory and applications

AU - Boccaletti, S

AU - Grebogi, C

AU - Lai, Y C

AU - Mancini, H

AU - Maza, D

AU - Lai, Ying-Cheng

N1 - The authors are grateful to F.T. Arecchi, E. Barreto, G. Basti, E. Bollt, A. Farini, R. Genesio, A. Giaquinta, S. Hayes, E. Kostelich, A.L. Perrone, F. Romeiras and T. Tél for many fruitful discussions. SB acknowledges financial support from the EEC Contract no. ERBFMBICT983466. CG was supported by DOE and by a joint Brasil-USA grant (CNPq/NSF-INT). YCL was supported by AFOSR under Grant No. F49620-98-1-0400 and by NSF under Grant No. PHY-9722156. HM and DM acknowledge financial support from Ministerio de Educacion y Ciencia (Grant N. PB95-0578) and Universidad de Navarra, Spain (PIUNA).

PY - 2000/5

Y1 - 2000/5

N2 - Control of chaos refers to a process wherein a tiny perturbation is applied to a chaotic system, in order to realize a desirable (chaotic, periodic, or stationary) behavior. We review the major ideas involved in the control of chaos, and present in detail two methods: the Ott-Grebogi-Yorke (OGY) method and the adaptive method. We also discuss a series of relevant issues connected with chaos control, such as the targeting problem, i.e., how to bring a trajectory to a small neighborhood of a desired location in the chaotic attractor in both low and high dimensions, and point out applications for controlling fractal basin boundaries. In short, we describe procedures for stabilizing desired chaotic orbits embedded in a chaotic attractor and discuss the issues of communicating with chaos by controlling symbolic sequences and of synchronizing chaotic systems. Finally, we give a review of relevant experimental applications of these ideas and techniques. (C) 2000 Elsevier Science B.V. All rights reserved.

AB - Control of chaos refers to a process wherein a tiny perturbation is applied to a chaotic system, in order to realize a desirable (chaotic, periodic, or stationary) behavior. We review the major ideas involved in the control of chaos, and present in detail two methods: the Ott-Grebogi-Yorke (OGY) method and the adaptive method. We also discuss a series of relevant issues connected with chaos control, such as the targeting problem, i.e., how to bring a trajectory to a small neighborhood of a desired location in the chaotic attractor in both low and high dimensions, and point out applications for controlling fractal basin boundaries. In short, we describe procedures for stabilizing desired chaotic orbits embedded in a chaotic attractor and discuss the issues of communicating with chaos by controlling symbolic sequences and of synchronizing chaotic systems. Finally, we give a review of relevant experimental applications of these ideas and techniques. (C) 2000 Elsevier Science B.V. All rights reserved.

KW - unstable periodic-orbits

KW - fractal basin boundaries

KW - resonant parametric perturbations

KW - time-delay autosynchronization

KW - Belousov-Zhabotinsky Reaction

KW - crisis-induced intermittency

KW - high-dimensional chaos

KW - dynamical-systems

KW - strange attractors

KW - adaptive recognition

U2 - 10.1016/S0370-1573(99)00096-4

DO - 10.1016/S0370-1573(99)00096-4

M3 - Article

SN - 0370-1573

VL - 329

SP - 103

EP - 197

JO - Physics Reports

JF - Physics Reports

IS - 3

ER -

The control of chaos: theory and applications

Abstract

Bibliographical note

Keywords

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