Summary

Proceedings of the 2012 International Symposium on Nonlinear Theory and its Applications

2012

Session Number:B1L-D

Session:

Number:344

A Theory on Noise-Induced Synchronization of Chaotic Oscillators

Wataru Kurebayashi,  Kantaro Fujiwara,  Hiroya Nakao,  Tohru Ikeguchi,  

pp.344-347

Publication Date:

Online ISSN:2188-5079

DOI:10.15248/proc.1.344

PDF download (307.9KB)

Phase description is an essential tool for analytically investigating synchronization phenomena of limit cycle oscillators. In this paper, introducing a new type of phase description, we discussed the noise-induced phase synchronization of strongly fluctuating oscillators such as chaotic oscillators. We derived a probability density function of phase differences between oscillators, which enables us to explore statistical properties of the synchronization phenomena.

[1] S. H. Strogatz and I. Stewart. Coupled oscillators and biological synchronization. Sci. Am., 269(6):102-109, 1993.

[2] I. Aihara. Modeling synchronized calling behavior of Japanese tree frogs. Phys. Rev. E, 80:011918, 2009.

[3] A. Takamatsu, T. Fujii, and I. Endo. Time delay effect in a living coupled oscillator system with the plasmodium of Physarum polycephalum. Phys. Rev. Lett., 85:2026-2029, Aug 2000.

[4] E. Brown, J. Moehlis, and P. Holmes. On the phase reduction and response dynamics of neural oscillator populations. Neural Comput., 16(4):673-715, 2004.

[5] Y. Kuramoto. Chemical oscillations, waves, and turbulence. Springer-Verlag, Berlin, 1984.

[6] M. Rosenblum, A. Pikovsky, and J. Kurths. Phase synchronization of chaotic oscillators. Phys. Rev. Lett., 76(11):1804-1807, 1996.

[7] C. Zhou, J. Kurths, I. Z. Kiss, and J. L. Hudson. Noise-enhanced phase synchronization of chaotic oscillators. Phys. Rev. Lett., 89(1):014101, Jun 2002.

[8] Y. Wang, Y. C. Lai, and Z. Zheng. Onset of colored-noise-induced synchronization in chaotic systems. Phys. Rev. E, 79(5):056210, 2009.

[9] T. Imai, H. Suetani, and T. Aoyagi. A phase reduction approach for synchronization of chaotic systems. IEICE Tech. Rep., 109(269):97-102, 2009.

[10] S. Hata, K. Arai, and H. Nakao. Stochastic phase description of fluctuating rhythmic elements. IEICE Tech. Rep., 110(82):135-139, 2010.

[11] J. T. C. Schwabedal, A. Pikovsky, B. Kralemann, and M. Rosenblum. Optimal phase description of chaotic oscillators. Phys. Rev. E, 85:026216, 2012.

[12] H. Nakao, J.-N. Teramae, D. S. Goldobin, and Y. Kuramoto. Effective long-time phase dynamics of limit-cycle oscillators driven by weak colored noise. Chaos, 20(3):3126, 2010.

[13] W. Kurebayashi, K. Fujiwara, and T. Ikeguchi. Colored noise induces synchronization of limit cycle oscillators. Europhys. Lett., 97:50009, 2012.

[14] K. Yoshimura, J. Muramatsu, P. Davis, T. Harayama, H. Okumura, S. Morikatsu, H. Aida, and A. Uchida. Secure key distribution using correlated randomness in lasers driven by common random light. Phys. Rev. Lett., 108:070602, 2012.