It is shown that Hamiltonian systems can exhibit the phenomenon of chaotic synchronization. Specific attention is paid to the standard map. Analytic synchronization conditions are derived and numerically verified for the standard map. We report on experimental studies of an analog electronic circuit realization of a ‘‘piecewise linear standard map.’’ When coupled appropriately to a duplicate circuit, chaotic synchronization is observed. The relevance of this study to synchronization in other Hamiltonian systems is discussed.
REFERENCES
1.
L. M.
Pecora
and T. L.
Carroll
, Phys. Rev. Lett.
64
, 821
(1990
).2.
L. M.
Pecora
and T. L.
Carroll
, Phys. Rev. A
44
, 2374
(1991
).3.
M. d. S.
Viera
, P.
Khoury
, A. J.
Lichtenberg
, M. A.
Lieberman
, W.
Wonchoba
, J.
Gullicksen
, J. Y.
Huang
, R.
Sherman
, and M.
Steinberg
, Int. J. Bifurcations Chaos
2
, 645
(1992
).4.
L. O.
Chua
, L.
Kocarev
, K.
Eckart
, and M.
Itoh
, Int. J. Bifurcations Chaos
2
, 705
(1992
).5.
K.
Cuomo
and A. V.
Oppenheim
, Phys. Rev. Lett.
71
, 65
(1993
).6.
N. F.
Rul’kov
, A. R.
Volkovskii
, A.
Rodríguez-Lozano
, E. D.
Río
, and M. G.
Velarde
, Int. J. Bifurcations Chaos
2
, 669
(1992
).7.
8.
A. J. Lichtenberg and M. A. Lieberman, Regular and Stochastic Motion (Springer, New York, 1983)
9.
I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Series, and Products (Academic, Orlando, 1980).
10.
11.
12.
T. L.
Carroll
and L. M.
Pecora
, Int. J. Bifurcations Chaos
2
, 659
(1992
).13.
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© 1994 American Institute of Physics.
1994
American Institute of Physics
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