Abstract
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.
Funder
Japan Society for the Promotion of Science
Japan Science and Technology Agency
Subject
General Mathematics,Engineering (miscellaneous),Computer Science (miscellaneous)
Reference65 articles.
1. The Geometry of Biological Time;Winfree,2001
2. Chemical Oscillations, Waves, and Turbulence;Kuramoto,1984
3. Synchronization: A Universal Concept in Nonlinear Sciences;Pikovsky,2001
4. Phase reduction approach to synchronisation of nonlinear oscillators
5. Mathematical Foundations of Neuroscience;Ermentrout,2010
Cited by
8 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献