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On the chaos synchronization phenomena. (English) Zbl 0936.37010

Summary: Chaos synchronization is an important problem in the nonlinear science. However, several phenomena can be found in the synchronization systems. Here, we discuss several phenomena involved with the chaos synchronization problem. Between the involved phenomena, one can find: complete, practical and partial synchronization. A feedback controller is used to illustrate such synchronization phenomena. The feedback was recently reported and involves robustness features. Such control actions can induce one more phenomena: the almost synchronization (AS). In addition, it is shown that the AS can be found if the master and slave models are strictly different.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
37N35 Dynamical systems in control
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[1] Femat, R.; Alvarez-Ramı́rez, J.; Gonález, J., Phys. lett. A, 224, 271, (1997)
[2] Femat, R.; Alvarez-Ramı́rez, J., Phys. lett. A, 236, 307, (1997)
[3] Pecora, L.M.; Carroll, T.L., Phys. rev. lett., 64, 821, (1990)
[4] M.B. Rosenblum, A.S. Pikovsky, J. Kurths, Phys. Rev. Lett. 76 (1996) 1804; 78 (1997) 4193.
[5] van Vreeswijk, C., Phys. rev. E, 54, 5522, (1996)
[6] Femat, R.; Capistrán-Tobı́as, J.; Solı́s-Perales, G., Phys. lett. A, 252, 27, (1999)
[7] Y.H. Chen, M.Y. Chou, Phys. Rev. E 50 (1994) 2331; J. Alvarez-Ramı́rez, Phys. Rev. E 50 (1994) 2339.
[8] Aguire, L.A.; Billings, S.A., Nonl. sci., 5, 189, (1995)
[9] M. Morari, E. Zafiriou, Robust Process Control, Prentice Hall, 1989, USA. · Zbl 0728.93031
[10] R. Femat, J. Alvarez-Ramı́rez, G. Fernández-Anaya, Physica D, submitted for publication.
[11] Abbott, L.F.; van Vreesweijk, C., Phys. rev. E, 48, 1483, (1993)
[12] Traub, R.D.; Wong, R.S.W., Science, 216, 745, (1983)
[13] Suykens, J.A.; Curran, P.F.; Vandewalle, J.; Chua, L.O., IEEE trans. on circ. and syst. I, 44, 891, (1997)
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.