Abstract
The synchronization of stable oscillations is a well-known non-linear phenomenon frequently found in nature and widely used in technology [1–5]. Under synchronization, one usually understands the ability of coupled oscillators to switch from an independent oscillation regime, characterized by beats, to a stable coupled oscillation regime with identical or rational frequencies, when the coupling constant increases.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Andronov, A., Vitt, A., Khaikin, S.: Theory of Oscillations. Pergamon Press, Oxford (1966)
Blekhman, I.I.: Synchronization in Science and Technology. ASME Press, New York (1988)
Lindsey, W.: Synchronization Systems in Communications and Control. Prentice-Hall, New Jersey (1972)
Pikovsky, A., Rosenblum, M., Kurths, J.: Synchronization. In: A Universal Concept in Nonlinear Sciences. Cambridge University Press, Cambridge (2001)
Fradkov, A.L.: Cybernetical Physics: From Control of Chaos to Quantum Control. Springer, Berlin (2007)
Haken, H.: Brain Dynamics: An Introduction to Models and Simulations. Springer Series in Synergetics. Springer, Berlin/Heidelberg (2008)
Haken, H.: Information and Self Organisation: A Macroscopic Approach to Complex Systems. Springer Series in Synergetics. Springer, Berlin/Heidelberg (2006)
Yamada, T., Fujisaka, H.: Prog. Theor. Phys. 70, 1240–1248 (1983)
Aframovich, V.S., Verichev, N.N., Rabinovich, M.I.: Izv. Vuzov, Radiofizika 29, 795–803 (1986)
Kolmogorov, A.N.: IEEE Trans. Inf. Theory IT-14, 662–664 (1968)
Yamada, T., Fujisaka, H.: Prog. Theor. Phys. 72, 885–894 (1984)
Pecora, L.M., Carroll, T.L., Johnson, G.A., Mar, D.J.: Chaos 7 (4), 520–543 (1997)
Pecora, L.M., Carroll, T.L.: Phys. Rev. A 44, 2374–2383 (1991)
Guemez, J., Matas, M.A., et al.: Phys. Rev. E 52, R2145–R2148 (1995)
Amritkar, R., Gupte, N.: Phys. Rev. E 47, 3889–3895 (1993)
Brown, R., Kocarev, L.: arXiv:chao-din/9811013 (1999)
Heagy, J.F., Carroll, T.L.: Chaos 4, 385–390 (1994)
Chirikov, B.V.: Phys. Rep. 52, 265–379 (1979)
Lai, Y.-C., Grebogi, C.: Phys. Rev. E 47, 2357–2360 (1993)
Parlitz, U.: Phys. Rev. Lett. 76, 1232–1235 (1996)
Verhulst, F.: Nonlinear Differential Equations and Dynamical Systems. Springer, Berlin (1996)
Toral, R., Mirasso, C., Hernandez-Garsia, E., Piro, O.: Chaos 11, 665–673 (2001)
Matsumoto, K., Tsuda, I.: J. Stat. Phys. 31, 87–106 (1983)
Yu, L., Ott, E., Chen, Q.: Phys. Rev. Lett. 65, 2935–2938 (1990)
Fahy, S., Hamman, D.: Phys. Rev. Lett. 69, 761–764 (1992)
Maritan, A., Banavar, J.: Phys. Rev. Lett. 72, 1451–1454 (1994)
Pikovsky, A.: Phys. Rev. Lett. 73, 2931–2932 (1994)
Herzel, H., Freund, J.: Phys. Rev. E 52, 3238–3241 (1995)
Lai, C.H., Zhou, C.: Europhys. Lett. 43, 376–380 (1988)
Kosarev, L., Tazev, Z., Stojanovski, T., Parlitz, U.: Chaos 7 (4), 635–643 (1997)
Kosarev, L., Tazev, Z., Parlitz, U.: Phys. Rev. Lett. 79, 51–54 (1997)
DeWitt, A., Dewel, G., Borckmans, P.: Phys. Rev. E 48, R4191–R4194 (1993)
Brown, R., Rulkov, N., Tufillaro, N.: Phys. Rev. E 50, 4488–4508 (1994)
Cuomo, K.M., Oppenheim, A.V.: Phys. Rev. Lett. 71, 65–68 (1993)
Kosarev, L., Halle, K.S., Eckert, K., et al.: Int. J. Bifurcation Chaos 2, 709–713 (1992)
Murali, K., Lakshmanan, M.: Phys. Rev. E 48, R1624–R1626 (1993)
Carroll, T.L., Pecora, L.M.: Physica D 67, 126–140 (1993)
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing Switzerland
About this chapter
Cite this chapter
Bolotin, Y., Tur, A., Yanovsky, V. (2017). Synchronization of Chaotic Systems. In: Chaos: Concepts, Control and Constructive Use. Understanding Complex Systems. Springer, Cham. https://doi.org/10.1007/978-3-319-42496-5_6
Download citation
DOI: https://doi.org/10.1007/978-3-319-42496-5_6
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42495-8
Online ISBN: 978-3-319-42496-5
eBook Packages: Physics and AstronomyPhysics and Astronomy (R0)