TY - JOUR
T1 - The control of chaos
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
VL - 329
SP - 103
EP - 197
JO - Physics Reports
JF - Physics Reports
SN - 0370-1573
IS - 3
ER -