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Anti-synchronization of chaotic oscillators. (English) Zbl 1098.37521

Summary: We have observed anti-synchronization phenomena in coupled identical chaotic oscillators. Anti-synchronization can be characterized by the vanishing of the sum of relevant variables. We have qualitatively analyzed its base mechanism by using the dynamics of the difference and the sum of the relevant variables in coupled chaotic oscillators. Near the threshold of the synchronization and anti-synchronization transition, we have obtained the novel characteristic relation.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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[1] Fujisaka, H.; Yamada, T., Prog. Theor. Phys., 69, 32 (1983) · Zbl 1171.70306
[2] Afraimovich, V. S.; Verichev, N. N.; Ravinovich, M. I., Radiophys. Quant. Electron., 29, 747 (1986), (English translation of Izv. Vyssh. Uchebn. Zaved. Radiofiz.)
[3] Pecora, L. M.; Carroll, T. L., Phys. Rev. Lett., 64, 821 (1990) · Zbl 0938.37019
[4] Maritan, A.; Banavar, J., Phys. Rev. Lett., 72, 1451 (1994)
[5] Longa, L.; Curado, E. M.F.; Oliveira, F. A., Phys. Rev. E, 54, R2201 (1996)
[6] Rim, S.; Hwang, D. U.; Kim, I.; Kim, C. M., Phys. Rev. Lett., 85, 2304 (2000)
[7] Volodchenko, K. V.; Ivanov, V. N.; Gong, S. H.; Choi, M.; Park, Y. J.; Kim, C. M., Opt. Lett., 26, 1406 (2001)
[8] Rosenblum, M. G.; Pikovsky, A. S.; Kurths, J., Phys. Rev. Lett., 78, 4193 (1997)
[9] Pikovsky, A. S.; Rosenblum, M.; Osipov, G. V.; Kurths, J., Physica D, 104, 219 (1997) · Zbl 0898.70015
[10] Güémez, J.; Martin, C.; Matias, M. A., Phys. Rev. E, 55, 124 (1997)
[11] Bennett, M.; Schatz, M. F.; Rockwood, H.; Wiesenfeld, K., Proc. R. Soc. A, 458, 563 (2002) · Zbl 1026.01007
[12] Sivaprakasam, S.; Pierce, I.; Rees, P.; Spencer, P. S.; Shore, K. A.; Valle, A., Phys. Rev. A, 64, 013805 (2001)
[13] Uchida, A.; Liu, Y.; Fischer, I.; Davis, P.; Aida, T., Phys. Rev. A, 64, 023801 (2001)
[14] Nakata, S.; Miyata, T.; Ojima, N.; Yoshikawa, K., Physica D, 115, 313 (1998) · Zbl 0962.76505
[15] Cao, L. Y.; Lai, Y. C., Phys. Rev. E, 58, 382 (1998)
[16] Alexander, J. C.; Yorke, J. A.; You, Z.; Kan, I., Int. J. Bifur. Chaos, 2, 795 (1992) · Zbl 0870.58046
[17] Ott, E.; Alexander, J. C.; Kan, I.; Sommerer, J. C.; Yorke, J. A., Physica D, 76, 384 (1994) · Zbl 0820.58043
[18] Kan, I., Bull. Am. Math. Soc., 31, 68 (1994) · Zbl 0853.58077
[19] Heagy, J. F.; Carroll, T. L.; Pecora, L. M., Phys. Rev. Lett., 73, 3528 (1994)
[20] Lai, Y.-C.; Grebogi, C., Phys. Rev. Lett., 77, 5047 (1996)
[21] Ding, M.; Yang, W., Phys. Rev. E, 52, 207 (1995)
[22] Haken, H., Phys. Lett. A, 53, 77 (1975)
[23] Biswas, D. R.; Harrison, R. G.; Weiss, C. O.; Klische, W.; Dangoise, D.; Glorieux, P.; Lawandy, N. M., (Arecchi, F. T.; Harrison, R. G., Instabilities and Chaos in Quantum Optics (1986), Springer: Springer Berlin), 109
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