Nonlinear Theory and Its Applications, IEICE
Online ISSN : 2185-4106
ISSN-L : 2185-4106
Special Section on Network Sciences and Engineering
A criterion for timescale decomposition of external inputs for generalized phase reduction of limit-cycle oscillators
Wataru KurebayashiSho ShirasakaHiroya Nakao
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2015 Volume 6 Issue 2 Pages 171-180

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Abstract

The phase reduction method is a dimension reduction method for weakly driven limit-cycle oscillators, which has played an important role in the theoretical analysis of synchronization phenomena. Recently, we proposed a generalization of the phase reduction method [W. Kurebayashi et al., Phys. Rev. Lett. 111, 2013]. This generalized phase reduction method can robustly predict the dynamics of strongly driven oscillators, for which the conventional phase reduction method fails. In this generalized method, the external input to the oscillator should be properly decomposed into a slowly varying component and remaining weak fluctuations. In this paper, we propose a simple criterion for timescale decomposition of the external input, which gives accurate prediction of the phase dynamics and enables us to systematically apply the generalized phase reduction method to a general class of limit-cycle oscillators. The validity of the criterion is confirmed by numerical simulations.

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© 2015 The Institute of Electronics, Information and Communication Engineers
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