Asymptotic Phase and Amplitude for Classical and Semiclassical Stochastic Oscillators via Koopman Operator Theory

The asymptotic phase is a fundamental quantity for the analysis of deterministic limit-cycle oscillators, and generalized definitions of the asymptotic phase for stochastic oscillators have also been proposed. In this article, we show that the asymptotic phase and also amplitude can be defined for c...

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Published inMathematics (Basel) Vol. 9; no. 18; p. 2188
Main Authors Kato, Yuzuru, Zhu, Jinjie, Kurebayashi, Wataru, Nakao, Hiroya
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.09.2021
Subjects
Amplitudes
Asymptotic properties
Eigenvalues
Eigenvectors
Koopman operator analysis
oscillations
Oscillators
stochastic systems
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Summary:The asymptotic phase is a fundamental quantity for the analysis of deterministic limit-cycle oscillators, and generalized definitions of the asymptotic phase for stochastic oscillators have also been proposed. In this article, we show that the asymptotic phase and also amplitude can be defined for classical and semiclassical stochastic oscillators in a natural and unified manner by using the eigenfunctions of the Koopman operator of the system. We show that the proposed definition gives appropriate values of the phase and amplitude for strongly stochastic limit-cycle oscillators, excitable systems undergoing noise-induced oscillations, and also for quantum limit-cycle oscillators in the semiclassical regime.
ISSN:2227-7390
2227-7390
DOI:10.3390/math9182188