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Title: Linear response theory for coupled phase oscillators with general coupling functions
Authors: Terada, Yu
Yamaguchi, Yoshiyuki Y
Author's alias: 山口, 義幸
Issue Date: 31-Jan-2020
Publisher: IOP Publishing
Journal title: Journal of Physics A: Mathematical and Theoretical
Volume: 53
Issue: 4
Thesis number: 044001
Abstract: We develop a linear response theory by computing the asymptotic value of the order parameter from the linearized equation of continuity around the nonsynchronized reference state using the Laplace transform in time. The proposed theory is applicable to a wide class of coupled phase oscillator systems and allows for any coupling functions, any natural frequency distributions, any phase-lag parameters, and any values for the time-delay parameter. This generality is in contrast to the limitation of the previous methods of the Ott–Antonsen ansatz and the self-consistent equation for an order parameter, which are restricted to a model family whose coupling function consists of only a single sinusoidal function. The theory is verified by numerical simulations.
Rights: This is an author-created, un-copyedited version of an article accepted for publication in 'Journal of Physics A: Mathematical and Theoretical'. The publisher is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
The full-text file will be made open to the public on 7 January 2021 in accordance with publisher's 'Terms and Conditions for Self-Archiving'.
This is not the published version. Please cite only the published version. この論文は出版社版でありません。引用の際には出版社版をご確認ご利用ください。
DOI(Published Version): 10.1088/1751-8121/ab5eaf
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