×

zbMATH — the first resource for mathematics

Generalized synchronization of continuous chaotic system. (English) Zbl 1083.37515
Summary: A sufficient condition for the generalized synchronization of continuous chaotic systems with a kind of nonlinear transformation is derived. The method is illustrated by applications to Lorenz and Duffing chaotic systems and the simulation results demonstrate the effectiveness of the proposed theorem.

MSC:
37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Fujisaka, H.; Yamada, T., Stability theory of synchronized motion in coupled-oscillator systems, Progr theor phys, 69, 32-47, (1983) · Zbl 1171.70306
[2] Pecora, L.M.; Carroll, T.L., Synchronization in chaotic system, Phys rev lett, 64, 821-824, (1990) · Zbl 0938.37019
[3] Wang, Y.; Guan, Z.-H.; Wang, H.O., Feedback and adaptive control for the synchronization of Chen system via a single variable, Phys lett A, 312, 34-40, (2003) · Zbl 1024.37053
[4] Fradkov, A.L.; Pogromsky, A.Yu., Speed gradient control of chaotic continuous-time systems, IEEE trans circuits syst I, 43, 11, 907-913, (1996)
[5] Nijmeijer, H.; Mareels, I.M.Y., An observer looks at synchronization, IEEE trans circuits syst I, 44, 10, 882-890, (1997)
[6] Itoh, M.; Yang, T.; Chua, L.O., Conditions for impulsive synchronization of chaotic and hyperchaotic systems, Int J bifur chaos, 11, 2, 551-560, (2001) · Zbl 1090.37520
[7] Wang, Y.-W.; Guan, Z.-H.; Xiao, J.-W., Impulsive synchronization for a class of continuous systems, Chaos, 14, 1, 199-203, (2004)
[8] Rulkov, N.F.; Sushchik, M.M.; Tsimring, L.S.; Abarbanel, H.D.I., Generalized synchronization of chaos in directionally coupled chaotic systems, Phys rev E, 51, 980-994, (1995)
[9] Kocarev, L.; Parlitz, U., Generalized synchronization, predictability and equivalence of unidirectionally coupled systems, Phys rev lett, 76, 11, 1816-1819, (1996)
[10] Abarbanel, H.D.I.; Rulkov, N.F.; Sushchik, M.M., Generalized synchronization of chaos: the auxiliary system approach, Phys rev E, 53, 4528-4535, (1996)
[11] Pyragas, K., Weak and strong synchronization of chaos, Phys rev E, 54, R4508-R4512, (1996)
[12] Parlitz, U.; Junge, L.; Kocarev, L., Subharmonic entrainment of unstable period orbits and generalized synchronization, Phys rev lett, 79, 17, 3158-3161, (1997)
[13] Parlitz, U.; Junge, L.; Kocarev, L., Nonidentical synchronization of identical systems, Int J bifur chaos, 9, 12, 2305-2309, (1999)
[14] Afraimovich V, Cordonet A, Rulkov NF. Generalized synchronization of chaos in noninvertible maps. Phys Rev E 2002;66:016208-1-6.
[15] Zhan M, Wang X, Gong X, Wei GW, Lai C-H. Complete synchronization and generalized synchronization of one-way coupled time-delay systems. Phys Rev E 2003;68:036208-1-5.
[16] Yang, T.; Chua, L.O., Generalized synchronization of chaos via linear transformations, Int J bifur chaos, 9, 1, 215-219, (1999) · Zbl 0937.37019
[17] Cincotti S, Teglio A. Generalized synchronization on linear manifold in coupled nonlinear systems. ISCAS 2002;3:III-61-4.
[18] Yang, X.S.; Chen, G., Some observer-based criteria for discrete-time generalized chaos synchronization, Chaos, solitons & fractals, 13, 1303-1308, (2002) · Zbl 1006.93580
[19] Liu, S.T.; Chen, G., Nonlinear feedback-controlled generalized synchronization of spatial chaos, Chaos, solitons & fractals, 22, 35-46, (2004) · Zbl 1060.93531
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.