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Authors
Kinzel, W.; Englert, A.; Kanter, I.

Digital Object Identifier (DOI)
10.3182/20090622-3-UK-3004.00048

Page Numbers:
252-255

Index Terms
No keywords available

Abstract
Networks of chaotic units with time delayed couplings and feedbacks are investigated analytically and numerically. Based on the results of simple models, three general conjectures are postulated, which need a rigorous proof (or counter example).

References

[1] L. M. Pecora and T. L. Carroll. Synchronization in
    chaotic systems. 64(8):821-824, 1990.
[2] A. Pikovsky, M. Rosenblum, and J. Kurths. Synchronization,
    a universal concept in nonlinear sciences. Cambridge
    University Press, Cambridge, 2001.
[3] L. Kocarev and U. Parlitz. General approach for chaotic
    synchronization with applications to communication. 74
    (25):5028-5031, 1995.
[4] For review see W. Kinzel and I. Kanter. Secure communication
    with chaos synchronization. In E. Schöll
    and H.G. Schuster, editors, Handbook of Chaos Control.
    Wiley-VCH, Weinheim, second edition, 2008.
[5] A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi,
    P. Colet, I. Fischer, J. García-Ojalvo, C. R. Mirasso,
    L. Pesquera, and K. A. Shore. Chaos-based communications
    at high bit rates using commercial fibre-optic links.
    438:343-346, 2005.
[6] S. Boccaletti, J. Kurths, G. Osipov, D. L. Valladares,
    and C. S. Zhou. The synchronization of chaotic systems.
    Physics Reports, 366:1-2, August 2002.
[7] S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-
    U. Hwang. Complex networks: Structure and dynamics.
    Physics Reports, 424:175-308, February 2006. doi: 10.
    1016/j.physrep.2005.10.009.
[8] Louis M. Pecora and Thomas L. Carroll. Master stability
    functions for synchronized coupled systems. Phys.
    Rev. Lett., 80(10):2109-2112, Mar 1998. doi: 10.1103/
    PhysRevLett.80.2109.
[9] I. Kanter J. Kestler, W. Kinzel. Sublattice synchronization
    of chaotic networks with delayed couplings. Phys.
    Rev. E, 76:035202, 2007.
[10] I. Kanter W. Kinzel J. Kestler, E. Kopelowitz. Patterns
     of chaos synchronization. 77(4):046209, 2008.
[11] E. Klein, N. Gross, M. Rosenbluh, W. Kinzel,
     L. Khaykovich, and I. Kanter. Stable isochronal synchronization
     of mutually coupled chaotic lasers. 73(6):
     066214, 2006.
[12] E. Klein, R. Mislovaty, I. Kanter, and W. Kinzel.
     Public-channel cryptography using chaos synchronization.
     72:016214, 2005.
[13] E. Klein, N. Gross, E. Kopelowitz, M. Rosenbluh,
     L. Khaykovich, W. Kinzel, and I. Kanter. Public-channel
     cryptography based on mutual chaos pass filters. Phys.
     Rev. E, 74(4):046201, 2006.
[14] I. Kanter, E. Kopelowitz, and W. Kinzel. Public Channel
     Cryptography: Chaos Synchronization and Hilbert's
     Tenth Problem. Physical Review Letters, 101(8):084102,
     August 2008. doi: 10.1103/PhysRevLett.101.084102.
[15] I. Stewart M. Golubitsky. Nonlinear dynamics of networks:
     the groupoid formalism. Bull. Am. Math. Soc,
     43:035202, 2006.
[16] M. Zigzag, M. Butkovski, A. Englert, W. Kinzel, and
     I. Kanter. Emergence of zero-lag synchronization in
     generic mutually coupled chaotic systems. Europhys.
     Lett. in print.
[17] W. Kinzel, A. Englert, G. Reents, M. Zigzag, and I. Kanter.
     Synchronization of networks of chaotic units with
     time-delayed couplings. to be published.