Summary

Proceedings of the 2013 International Symposium on Nonlinear Theory and its Applications

2013

Session Number:C2L-C

Session:

Number:413

Noise Effects on Generalized Chaos Synchronization in Semiconductor Lasers

Kenichi Arai,  Susumu Shinohara,  Satoshi Sunada,  Kazuyuki Yoshimura,  Takahisa Harayama,  Atsushi Uchida,  

pp.413-416

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.2.413

PDF download (333.4KB)

Summary:
We investigate the effects of noise in drive and/or response systems on generalized synchronization. We show numerically that noise in a drive system can induce synchronization in an unidirectionally coupled Lorenz system, while noise in a response system disrupts the synchronization. In addition, through experiments using coupled semiconductor lasers with optical feedback, we observe that noise in a drive system enhances the synchronization.

References:

[1] Hirokazu Fujisaka and Tomoji Yamada. Stability theory of synchronized motion in coupled-oscillator systems. Progress of Theoretical Physics, Vol. 69, No. 1, pp. 32-47, 1983.

[2] Tomoji Yamada and Hirokazu Fujisaka. Stability theory of synchronized motion in coupled-oscillator systems. II. Progress of Theoretical Physics, Vol. 70, No. 5, pp. 1240-1248, 1983.

[3] Tomoji Yamada and Hirokazu Fujisaka. Stability theory of synchronized motion in coupled-oscillator systems. III. Progress of Theoretical Physics, Vol. 72, No. 5, pp. 885-894, 1984.

[4] Kevin M Cuomo and Alan V Oppenheim. Circuit implementation of synchronized chaos with applications to communications. Physical Review Letters, Vol. 71, No. 1, pp. 65-68, 1993.

[5] Kevin M Cuomo, Alan V Oppenheim, and Steven H Strogatz. Synchronization of Lorenz-based chaotic circuits with applications to communications. Circuits and systems II: Analog and digital signal processing, IEEE Transactions on, Vol. 40, No. 10, pp. 626-633, 1993.

[6] Gregory D Vanwiggeren and Rajarshi Roy. Communication with chaotic lasers. Science, Vol. 279, No. 5354, pp. 1198-1200, 1998.

[7] Kazuyuki Yoshimura, Jun Muramatsu, Peter Davis, Takahisa Harayama, Haruka Okumura, Shinichiro Morikatsu, Hiroki Aida, and Atsushi Uchida. Secure key distribution using correlated randomness in lasers driven by common random light. Physical Review Letters, Vol. 108, No. 7, p. 70602, 2012.

[8] Daniel J Gauthier and Joshua C Bienfang. Intermittent loss of synchronization in coupled chaotic oscillators: Toward a new criterion for high-quality synchronization. Physical Review Letters, Vol. 77, No. 9, pp. 1751-1754, 1996.

[9] Alexander E Hramov and Alexey A Koronovskii. Intermittent generalized synchronization in unidirectionally coupled chaotic oscillators. EPL (Europhysics Letters), Vol. 70, No. 2, p. 169, 2007.

[10] Kenji Matsumoto and Ichiro Tsuda. Noise-induced order. Journal of Statistical Physics, Vol. 31, No. 1, pp. 87-106, 1983.

[11] Amos Maritan and Jayanth R Banavar. Chaos, noise, and synchronization. Physical Review Letters, Vol. 72, No. 10, pp. 1451-1454, 1994.

[12] C H Lai and Changsong Zhou. Synchronization of chaotic maps by symmetric common noise. Europhysics Letters, Vol. 43, No. 4, p. 376, 2007.

[13] Raúl Toral, Claudio R Mirasso, Emilio Hernández-García, and Oreste Piro. Analytical and numerical studies of noise-induced synchronization of chaotic systems. Chaos (Woodbury, NY), Vol. 11, No. 3, p. 665, 2001.

[14] Changsong Zhou and Jürgen Kurths. Noise-induced phase synchronization and synchronization transitions in chaotic oscillators. Physical Review Letters, Vol. 88, No. 23, p. 230602, 2002.

[15] Zachary F Mainen, Terrence J Sejnowski, et al. Reliability of spike timing in neocortical neurons. Science, Vol. 268, No. 5216, pp. 1503-1506, 1995.

[16] Atsushi Uchida, Ryan McAllister, and Rajarshi Roy. Consistency of nonlinear system response to complex drive signals. Physical Review Letters, Vol. 93, No. 24, p. 244102, 2004.

[17] Nikolai F Rulkov, Mikhail M Sushchik, Lev S Tsimring, and Henry DI Abarbanel. Generalized synchronization of chaos in directionally coupled chaotic systems. Physical Review E, Vol. 51, No. 2, p. 980, 1995.

[18] Henry DI Abarbanel, Nikolai F Rulkov, and Mikhail M Sushchik. Generalized synchronization of chaos: The auxiliary system approach. Physical Review E, Vol. 53, No. 5, p. 4528, 1996.

[19] Kestutis Pyragas. Weak and strong synchronization of chaos. Physical Review E, Vol. 54, No. 5, pp. 4508-4511, 1996.