×

Synchronization of unidirectional coupled chaotic systems via partial stability. (English) Zbl 1048.37027

Summary: Chaos synchronization can be achieved by several methods but there is no easy unified criterion in general. A general scheme is proposed to achieve chaos synchronization via stability with respect to partial variables. Three theorems for synchronization of unidirectional coupled nonautonomous (also autonomous) systems by linear feedback are developed for systems with and without system structure perturbations. The system, fly-ball governor, is demonstrated as an example.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
34C28 Complex behavior and chaotic systems of ordinary differential equations
93D15 Stabilization of systems by feedback
PDF BibTeX XML Cite
Full Text: DOI

References:

[1] Fujisaka, H.; Yamada, Prog. theor. phys., 69, 32, (1983)
[2] Afraimovich, V.S.; Verichev, N.N.; Robinovich, M.I., Radiophys. quantum electron., 29, 795, (1986)
[3] Pecora, L.M.; Carroll, T.L., Phys. rev. lett., 64, 821, (1990)
[4] Pecora, L.M.; Carroll, T.L., Phys. rev. A, 44, 2374, (1991)
[5] He, R.; Vaidya, P.G., Phys. rev. A, 46, 7387, (1992)
[6] Pecora, L.M.; Carroll, T.L., Physica D, 67, 126, (1993)
[7] Ding, M.; Ott, Phys. rev. E, 49, 945, (1994)
[8] Murali, K.; Lakshmanan, M., Phys. rev. E, 49, 4882, (1994)
[9] Wu, C.W.; Chua, L.O., Int. J. bifurcat. chaos, 4, 979, (1994)
[10] Carroll, T.L.; Pecora, L.M., IEEE trans. circ. syst., 40, 646, (1993)
[11] Pyragas, K., Phys. rev. E, 54, 4508, (1996)
[12] Kapitaniak, T.; Sekieta, M.; Ogorzolek, M., Int. J. bifurcat. chaos, 6, 211, (1996)
[13] Carroll, T.L.; Pecora, L.M., Int. J. bifurcat. chaos, 9, 2315, (1999)
[14] Santoboni, G.S.; Bishop, S.R.; Varone, A., Int. J. bifurcat. chaos, 9, 2345, (1999)
[15] Kocarev, L.; Parlitz, U.; Brown, R., Phys. rev. E, 61, 3716, (2000)
[16] Carroll, T.L.; Pecora, L.M., IEEE trans. CAS, 38, 453, (1991)
[17] Cuomo, K.M.; Oppenheim, A.V., Phys. rev. lett., 71, 65, (1993)
[18] Wu, C.W.; Chua, L., Int. J. bifurcat. chaos, 3, 1619, (1993)
[19] Short, K.M., Int. J. bifurcat. chaos, 4, 959, (1994)
[20] Perez, G.; Cerdeira, H.A., Phys. rev. lett., 74, 1970, (1995)
[21] Cuomo, K.M., Int. J. bifurcat. chaos, 3, 1327, (1993)
[22] Cuomo, K.M.; Oppenheim, A.V.; Strogatz, S.H., IEEE trans. circ. syst., 40, 626, (1993)
[23] Peng, J.H.; Ding, E.J.; Ding, M.; Yang, W., Phys. rev. lett., 76, 904, (1996)
[24] Lü, J.; Zhou, T.; Zhang, S., Chaos, solitons & fractals, 14, 529, (2002)
[25] Vaidya, P.G., Chaos, solitons & fractals, 17, 443, (2003)
[26] Morgül, O.; Solak, E., Phys. rev. E, 54, 4803, (1996)
[27] Grassi, G.; Mascolo, S., IEEE trans. circ. syst.-I, 44, 1011, (1997)
[28] Grassi, G.; Mascolo, S., Int. J. bifurcat. chaos, 9, 1175, (1999)
[29] Grassi, G.; Mascolo, S., IEEE trans. circ. syst.-II, 46, 478, (1999)
[30] Kozlov, A.K.; Shalfeev, V.D.; Chua, L.O., Int. J. bifurcat. chaos, 6, 569, (1999)
[31] di Bernardo, M., Phys. lett. A, 214, 139, (1996)
[32] di Bernardo, M., Int. J. bifurcat. chaos, 6, 557, (1996)
[33] Fradkov, A.L.; Markov, A.Yu., IEEE trans. circ. syst.-I, 44, 905, (1997)
[34] Wang, C.; Ge, S.S., Int. J. bifurcat. chaos, 11, 1743, (2001)
[35] Hong, Y.-G.; Qin, H.-S.; Chen, G.-R., Int. J. bifurcat. chaos, 11, 1149, (2001)
[36] Wang, C.; Ge, S.S., Chaos, solitons & fractals, 12, 1199, (2001)
[37] Chen, S.; Lü, J., Chaos, solitons & fractals, 14, 643, (2002)
[38] Tan, X.; Zhang, J.; Yang, Y., Chaos, solitons & fractals, 16, 37, (2003)
[39] Fang, J.-Q.; Hong, Y.-G.; Chen, G.-R., Phys. rev. E, 59, R2523, (1999)
[40] Grassi, G.; Mascolo, S., Int. J. bifurcat. chaos, 9, 705, (1999)
[41] Tonelli, R.; Lai, Y.-C.; Grebogi, C., Int. J. bifurcat. chaos, 10, 2611, (2000)
[42] Wang, X.-F.; Wang, Z.-Q.; Chen, G.-R., Int. J. bifurcat. chaos, 9, 1169, (1999)
[43] Yu, X.-H.; Song, Y.-X., Int. J. bifurcat. chaos, 11, 1737, (2001)
[44] Hegazi, A.S.; Agiza, H.N.; Ei Dessoky, M.M., Chaos, solitons & fractals, 12, 1091, (2001)
[45] Liu, F., Chaos, solitons & fractals, 13, 723, (2002)
[46] Codreanu, S., Chaos, solitons & fractals, 15, 507, (2003)
[47] Chen, M.; Han, Z., Chaos, solitons & fractals, 17, 709, (2003)
[48] Rulkov, N.F., Phys. rev. E, 51, 980, (1995)
[49] Abarbanel, H.D.I.; Rulkov, N.F.; Sushchik, M.M., Phys. rev. E, 53, 4528, (1996)
[50] Kocarev, L.; Parlitz, U., Phys. rev. lett., 76, 1816, (1996)
[51] Pecora, L.M.; Carroll, T.L.; Heagy, J.F., Phys. rev. E, 52, 3420, (1995)
[52] Hunt, B.R.; Ott, E.; Yorke, J.A., Phys. rev. E, 55, 4029, (1997)
[53] Lu, J.; Xi, Y., Chaos, solitons & fractals, 17, 825, (2003)
[54] Josić, K., Phys. rev. lett., 80, 3053, (1996)
[55] Rumjantsev, V.V., Vestnik moskov. univ. ser. I mat. meh., 4, 9, (1957)
[56] Rouche N, Habets P, Laloy M. Stability Theory by Liapunov’s direct method, 1977 · Zbl 0364.34022
[57] Rumjantsev, V.V.; Oziraner, A.S., Stability and stabilization of motion with respect to part of the variables, (1987), Nauka, [in Russian] · Zbl 0626.70021
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.