×

zbMATH — the first resource for mathematics

Generalized synchronization of chaos in electronic circuit experiments. (English) Zbl 0930.37014
Summary: Two examples of one-way coupled electronic circuits displaying generalized synchronization of chaos are considered. In one of them, the dynamics of both the response and the driving systems represent a double-scroll chaos oscillator. In another example, the double-scroll oscillator is driven by an electronic analog of the Mackey-Glass system. To detect the generalized synchronization, an auxiliary response system that is a replica of the original one is used. In these systems, we have discovered two types of generalized synchronization, namely, a strong and a weak synchronization, which correspond to the existence of a smooth and a nonsmooth map from the trajectories of the driving attractor to the trajectories of the response system, respectively.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N20 Dynamical systems in other branches of physics (quantum mechanics, general relativity, laser physics)
37N99 Applications of dynamical systems
94C99 Circuits, networks
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Hayes, S.; Grebogy, C.; Ott, E.; Cuomo, K.M.; Oppenheim, A.V.; Kapitaniak, T.; Perec, G.; Cerdeira, H.A.; Peng, J.H.; Ding, E.J.; Ding, M.; Yang, W., Phys. rev. lett., Phys. rev. lett., Phys. rev. E, Phys. rev. lett., Phys. rev. lett., 76, 904, (1996)
[2] Brown, R.; Rulkov, N.F.; Tracy, E.R., Phys. rev. E, 49, 3784, (1994)
[3] Parlitz, U., Phys. rev. lett., 76, 1232, (1996)
[4] Winful, H.G.; Rahman, L., Phys. rev. lett., 65, 1575, (1990)
[5] Bayly, P.V.; Johnson, E.E.; Wolf, P.D.; Greenside, H.S.; Smith, W.M.; Ideker, R.E., J. cardiovas. electrophysiol., 4, 533, (1993)
[6] Pecora, L.M.; Carrol, T.L., Phys. rev. lett., 64, 821, (1990)
[7] Fujisaka, H.; Yamada, T.; Pyragas, K.; Carrol, T.L., Progr. theor. phys., Phys. lett. A, Phys. rev. E, 50, 2580, (1994)
[8] Kocarev, L.; Parlitz, U., Phys. rev. lett., 76, 1816, (1996)
[9] Rosenblum, M.G.; Pikovsky, A.S.; Kurths, J., Phys. rev. lett., 76, 1804, (1996)
[10] Afraimovich, V.S.; Verichev, M.M.; Rabinovich, M.I., Radiophys. quantum electron., 29, 795, (1986)
[11] Rulkov, N.F.; Sushchik, M.M.; Tsimring, L.S.; Abarbanel, H.D.I., Phys. rev. E, 51, 980, (1995)
[12] Abarbanel, H.D.I.; Rulkov, N.F.; Sushchik, M.M., Phys. rev. E, 53, 4528, (1996)
[13] Pyragas, K., Phys. rev. E, 54, R4508, (1996)
[14] Pecora, L.M.; Carrol, T.L., Phys. rev. A, 44, 2374, (1991)
[15] Rulkov, N.F.; Sushchik, M.M.; Rulkov, N.F., Phys. lett. A, Chaos, 6, 262, (1996)
[16] Yu, L.; Ott, E.; Chen, Q.; Pikovsky, A.S., Phys. rev. lett., Phys. lett. A, 165, 33, (1992)
[17] Ding, M.; Grebogi, C.; Ott, E.; Sauer, T.; Yorke, J.A., Physica D, 69, 404, (1993)
[18] T. Sauer and J.A. Yorke, Ergodic Theory Dyn. Syst., to appear.
[19] Landa, P.; Rosenblum, M., Sov. phys. dokl., 37, 237, (1992)
[20] Kaplan, J.L.; Yorke, J.A., (), 204
[21] Badii, R.; Broggi, G.; Derighetti, B.; Ravani, M.; Ciliberto, S.; Politi, A.; Rubio, M.A., Phys. rev. lett., 60, 979, (1988)
[22] Takens, F.; Abarbanel, H.D.I.; Brown, R.; Sidorovich, J.J.; Tsimring, L.S., (), Rev. mod. phys., 65, 1331, (1994)
[23] Sano, M.; Sawada, Y., Phys. rev. E, 55, (1985)
[24] K. Pyragas, Phys. Rev. E, submitted.
[25] Shinriki, M.; Yamamoto, M.; Mori, S., (), 394
[26] Kittel, A.; Pyragas, K.; Richter, R., Phys. rev. E, 50, 262, (1994)
[27] Press, W.H.; Flannery, B.P.; Teukolsky, S.A.; Vetterling, W.T., Numerical recipes, the art of scientific computing, (1990), Cambridge University Press Cambridge
[28] Grassberger, P.; Procaccia, I., Phys. rev. lett., 50, 346, (1983)
[29] Mackey, M.C.; Glass, L., Science, 197, 287, (1977)
[30] Namajūnas, A.; Pyragas, K.; Tamaševičius, A., Phys. lett. A, 201, 42, (1995)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.