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On a system of hyperstable frequency locking persistence under white noise

Published online by Cambridge University Press:  01 April 2000

MINPING QIAN  and
DAI WANG
MINPING QIAN
Affiliation:
Department of Probability and Statistics, Peking University, Beijing 100871, P. R. China (e-mail: qianmp@ssx0.math.pku.edu.cn)
DAI WANG
Affiliation:
Department of Probability and Statistics, Peking University, Beijing 100871, P. R. China (e-mail: qianmp@ssx0.math.pku.edu.cn)
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Abstract

This paper studies a special system of $N$-coupled oscillators under white noise. It is shown that we can get a positive recurrent diffusion process by winding the solution of this system on a cylinder along a special direction. Thus defining the rotation number as the limit of the frequency of the oscillator, we can prove that the rotation number exists and the frequency locking is successful no matter how large the white noise is.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 20 , Issue 2 , April 2000 , pp. 547 - 555
Copyright
© 2000 Cambridge University Press

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