A mechanism is proposed for synchronizing the chaotic vibrations of an externally forced array of oscillators with nearest-neighbor viscoelastic coupling. The proposed mechanism involves the application of small time-dependent perturbations to the individual oscillators. The perturbations required to preserve the coherence are of the order of magnitude of any noise present. The mechanism works with any form of external forcing. A modification of the mechanism is used to control the forced chaotic vibrations of a single Duffing oscillator allowed to vibrate out of the vertical plane.

1.
Aranson
I.
,
Golomb
D.
, and
Sompolinsky
H.
,
1992
, “
Spatial Coherence and Temporal Chaos in Macroscopic Systems with Asymmetrical Couplings
,”
Physical Review Letters
, Vol.
68
, pp.
3495
3498
.
2.
Auerbach
D.
,
1994
, “
Controlling Extended Systems of Chaotic Elements
,”
Physical Review Letters
, Vol.
72
, pp.
1184
1187
.
3.
Barratt
C.
,
1996
, “
Comment on ’Controlling Extended Systems of Chaotic Elements’ by D. Auerbach
,”
Physical Review Letters
, Vol.
76
, p.
712
712
.
4.
Braiman
Y.
, and
Goldhirsch
I.
,
1991
, “
Taming Chaotic Dynamics with Weak Periodic Perturbations
,”
Physical Review Letters
, Vol.
66
, pp.
2545
2548
.
5.
Brown, R., Rilkov, N. F., and Tufillaro, N. B., 1994, “The Effects of Additive Noise and Drift in the Dynamics of the Driving on Chaotic Synchronization,” Physics Letters A196, pp. 201–205.
6.
Carroll, T. L., and Pecora, L. M., 1993, “Cascading Synchronized Chaotic Systems,” Physica D67, pp. 126–140.
7.
Chacon
R.
, and
Bejarano
J. D.
,
1993
, “
Routes to Suppressing Chaos by Weak Periodic Perturbations
,”
Physical Review Letters
, Vol.
71
, pp.
3103
3106
.
8.
Davies, M. A., and Moon, F. C., 1993, “Transition from Soliton to Chaotic Motion during Impact of a Nonlinear Structure,” Cornell Univ. preprint.
9.
Ditto
W. L.
,
Rauseo
S. N.
, and
Spano
M. L.
,
1990
, “
Experimental Control of Chaos
,”
Physical Review Letters
, Vol.
65
, pp.
3211
3214
.
10.
Garfinkel
A.
,
Spano
M. L.
,
Ditto
W. L.
, and
Weiss
J. N.
,
1992
, “
Controlling Cardiac Chaos
,”
Science
, Vol.
257
, pp.
1230
1235
.
11.
Heagy, J. F., Carroll, T. L., and Pecora, L. M., 1994, “Synchronous Chaos in Coupled Oscillator Systems,” Physical Review E50, pp. 1874–1885.
12.
Ho, M. C., Chern, J. L., and Wang, D. P., 1994, “Creating the Desired Output Waveform in Nonlinear Oscillators with Modulations,” Physics Letters A194, pp. 159–164.
13.
Lai, Y. C., and Grebogi, C., 1993, Physical Review E47, 2357.
14.
Leven, R. W., and Koch, B. P., 1981, “Chaotic Behavior of a Parametrically Excited Damped Pendulum,” Physics Letters A86, pp. 71–74.
15.
McLaughlin
J. B.
,
1981
, “
Period-Doubling Bifurcations and Chaotic Motion for a Parametrically Forced Pendulum
,”
Journal of Statistical Physics
, Vol.
24
, pp.
375
388
.
16.
Moon, F. C., 1987, Chaotic Vibrations: An Introduction for Applied Scientists and Engineers, John Wiley & Sons.
17.
Moon
F. C.
,
1991
, “
Symbolic Dynamic Maps of Spatio-Temporal Chaotic Vibrations in a String of Impact Oscillators
,”
Chaos
, Vol.
1
, pp.
65
68
.
18.
Ott
E.
,
Grebogi
C.
, and
Yorke
J. A.
,
1990
, “
Controlling Chaos
,”
Physical Review Letters
, Vol.
64
, pp.
1196
1199
.
19.
Pecora, L. M., and Carroll, T. L., 1991a, “Driving Systems with Chaotic Signals,” Physical Review A44, pp. 2374–2383.
20.
Pecora
L. M.
, and
Carroll
T. L.
,
1991
b, “
Pseudoperiodic Driving: Eliminating Multiple Domains of Attraction using Chaos
,”
Physical Review Letters
, Vol.
67
, pp.
945
948
.
21.
Singer
J.
,
Wang
Y. Z.
, and
Bau
H. H.
,
1991
, “
Controlling a Chaotic System
,”
Physical Review Letters
, Vol.
66
, pp.
1123
1125
.
22.
Spano, M. L., Ditto, W. L., and Rauseo, S. N., 1991, “Exploitation of Chaos for Active Control,” Recent Advances in Active Control of Sound and Vibration, April 15–17.
23.
Sugawara
T.
,
Tachikawa
M.
,
Tsukamoto
T.
, and
Shimizu
T.
,
1994
, “
Observation of Synchronization in Laser Chaos
,”
Physical Review Letters
, Vol.
72
, pp.
3502
3505
.
24.
Umberger, D. K., Grebogi, C., Ott, E., and Afeyan, B., 1989, “Spatiotemporal Dynamics in a Dispersively Coupled Chain of Nonlinear Oscillators,” Physical Review A39, pp. 4835–4842.
25.
Wolf, A., Swift, J. B., Swinney, H. L., and Vastano, J. A., 1985, “Determining Lyapunov Exponents from a Time Series,” Physica 16D, pp. 285–317.
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