Abstract
Pairs of delay-coupled chaotic systems were shown to be able to achieve isochronal synchronization under bidirectional coupling and self-feedback. Such identical-in-time behavior was demonstrated to be stable under a set of conditions and to support simultaneous bidirectional communication between pairs of chaotic oscillators coupled with time-delay. More recently, it was shown that isochronal synchronization can emerge in networks with several hundreds of oscillators, which allows its exploitation for communication in distributed systems. In this paper, we introduce a conceptual framework for the application of isochronal synchronization to TDMA communication in networks of delay-coupled chaotic oscillators. On the basis of the stable and identical-in-time behavior of delay-coupled chaotic systems, the chaotic dynamics of distributed oscillators is used to support and sustain coordinate communication among nodes over the network. On the basis of the unique features of chaotic systems in isochronal synchronization, the chaotic signals are used to timestamp clock readings at the physical layer such that logical clock synchronization among the nodes (a prerequisite for TDMA) can be exploited using the same basic structure. The result is a standalone network communication scheme that can be advantageously applied in the context of ad-hoc networks or alike, especially short-ranged ones that yield low values of time-delay. As explored to its depths in practical implementations, this conceptual framework is argued to have potential to provide gain in simplicity, security and efficiency in communication schemes for autonomous/standalone network applications.
Similar content being viewed by others
References
M.S. Baptista, E.E.N. Macau, C. Grebogi, Y.C. Lai, E. Rosa Jr., Phys. Rev. E 62, 4835 (2000)
A. Argyris, D. Syvridis, L. Larger, V. Annovazzi-Lodi, P. Colet, I. Fischer, J. Garcia-Ojalvo, C.R. Mirasso, L. Pesquera, K.A. Shore, Nature 438, 343 (2005)
A. Argyris, E. Grivas, M. Hamacher, A. Bogris, D. Syvridis, Opt. Expr. 18, 5188 (2010)
U. Parlitz, T. Kocarev, T. Stojanovski, H. Preckel, Phys. Rev. E 53, 4351 (1996)
C. Grebogi, Y.C. Lai, Syst. Control Lett. 31, 307 (1997)
M.S. Baptista, E. Rosa Jr., C. Grebogi, Phys. Rev. E 61, 3590 (2000)
S. Hayes, C. Grebogi, E. Ott, Phys. Rev. Lett. 70, 3031 (1993)
J.M.F. Avila, J.R. Rios Leite, Opt. Lett. 17, 21442 (2009)
T. Deng, G.Q. Xia, L.P. Cao, J.G. Chen, X.D. Lin, Z.M. Wu, Opt. Commun. 282, 2243 (2009)
Y. Xia, C.K. Tse, F.C.M. Lau, IEEE Trans. Circuit Syst. II 51, 580 (2004)
R.M. Lopez-Gutierrez, C. Posadas-Castillo, Lopez-Mancilla, C. Cruz-Hernandez, Chaos, Solitons Fractals 41, 277 (2009)
J.M. Liu, H.F. Chen, S. Tang, IEEE Trans. Circuit Syst. I 48, 1475 (2001)
K.M. Cuomo, A.V. Oppenheim, Phys. Rev. Lett. 71, 65 (1993)
K.M. Cuomo, A.V. Oppenheim, S.H. Strogatz, IEEE Trans. Circuits Syst. Express Briefs 40, 634 (1993)
A. Wagemakers, J.M. Buldu, M.A.F. Sanjuan, Chaos 17, 023128 (2007)
R. Vicente, C.R. Mirasso, I. Fischer, Opt. Lett. 32, 403 (2007)
B.B. Zhou, R. Roy, Phys. Rev. E 75, 026205 (2007)
A. Wagemakers, J.M. Buldu, M.A.F. Sanjuan, Europhys. Lett. 81, 40005 (2008)
I. Kanter, E. Kopelowitz, W. Kinzel, Phys. Rev. Lett. 101, 084102 (2008)
E. Klein, N. Gross, M. Rosenbluh, W. Kinzel, L. Khaytovich, I. Kanter, Phys. Rev. E 73, 066214 (2006)
N. Jiang, W. Pan, B. Luo, L. Yan, S. Xiang, L. Yang, D. Zheng, N. Li, Phys. Rev. E 81, 066217 (2010)
T. Oguchi, H. Nijmeijer, T. Yamamoto, Proc. Eur. Contr. Conf., 3056 (2007)
T. Oguchi, H. Nijmeijer, T. Yamamoto, Chaos 18, 037108 (2008)
T. Oguchi, H. Nijmeijer, T. Yamamoto, T. Kniknie, Synchr. Four Identical Nonlinear Syst. Time-delay, 12153 (2008)
J.M.V. Grzybowski, E.E.N. Macau, T. Yoneyama, J. Phys. A: Math. Theor. 44, 175103 (2011)
J.M.V. Grzybowski, E.E.N. Macau, T. Yoneyama, Chaos 22, 033152 (2012)
R. Fan, I. Chakraborty, N.A. Lynch, Proc. OPODIS 67, 400 (2004)
Q. Li, D. Rus, IEEE Trans. Comput. 55, 214 (2006)
B. Sundararaman, U. Buy, A.D. Kshemkalyani, Ad Hoc Networks 3, 281 (2005)
C. Lenzen, T. Locher, P. Sommer, R. Wattenhofer, Clock synchronization: open problems in theory and practice, Lect. Notes in Comput. Sci. (Springer, 2000)
K.V. Prasad, Principles of digital communication systems and computer networks (Charles River Media, 2004)
S. Leffer, Comput. Lab. Seminar, 1 (2009)
E.N. Lorenz, J. Atmospheric Sci. 20, 130 (1963)
M.S. Baptista, E.E.N. Macau, C. Grebogi, Acta Astronaut. 54, 153 (2004)
E.E.N. Macau, C. Marinho, Acta Astronaut. 53, 465 (2003)
C.M.P. Marinho, E.E.N. Macau, T. Yoneyama, Acta Astronaut. 57, 230 (2005)
E.E.N. Macau, M.S. Baptista, C. Grebogi, Chaos (Woodbury) 13, 145 (2003)
A. Islam, Julkarnain, A. Kader, Int. J. Elec. Comp. Sci. 10, 13 (2010)
M. Itoh, L.O. Chua, Multiplexing Techniques via Chaos, 905 (1997)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Grzybowski, J., Macau, E. & Yoneyama, T. Isochronal synchronization in networks and chaos-based TDMA communication. Eur. Phys. J. Spec. Top. 223, 1447–1463 (2014). https://doi.org/10.1140/epjst/e2014-02146-6
Received:
Revised:
Published:
Issue Date:
DOI: https://doi.org/10.1140/epjst/e2014-02146-6