Progress of Theoretical Physics
Supplement No.161 (2006) pp. 360-363
URL : http://ptp.ipap.jp/link?PTPS/161/360/
DOI : 10.1143/PTPS.161.360

Noise Induced Phase Synchronization of a General Class of Limit Cycle Oscillators

Jun-nosuke Teramae¹ and Dan Tanaka²

(Received July 1, 2005)

We consider the effect of weak additive noise to a general class of limit cycle oscillators. Employing phase reduction method, the largest Lyapunov exponent of the noise driven oscillators are shown to be negative for a broad class of oscillators, which implies that identical limit cycle oscillators driven by a common additive noise can achieve phase synchronization without direct mutual interactions. Generalization of the results including the effect of colored noise and the effect of noise to spatially extended systems are also discussed.

References:

1. Y. Kuramoto, Chemical Oscillation, Waves, and Turbulence (Springer-Verlag, Tokyo, 1984; Dover Edition, 2003).
2. A. S. Pikovsky, in Nonlinear and Turbulent Processes in Physics, ed. R. Z. Sagdeev (Harwood, Singapore, 1984), p. 1601.
3. J. Teramae and D. Tanaka, Phys. Rev. Lett. 93 (2004), 204103[APS].
4. K. Nagai, H. Nakao and Y. Tsubo, Phys. Rev. E 71 (2005), 036217[APS].
5. D. S. Goldobin and A. Pikovsky, Phys. Rev. E 71 (2005), 045201[APS]; Physica A 351 (2005), 126[CrossRef].
6. Z. F. Mainen and T. J. Sejnowski, Science 268 (1995), 1503[Science].
7. L. Yu, E. Ott and Q. Chen, Phys. Rev. Lett. 65 (1990), 2935[APS].

Quick Search:

Copyright (c) Progress of Theoretical Physics 2010 All rights reserved.
ptp@yukawa.kyoto-u.ac.jp