基于Koopman算子理论的经典和半经典随机振子的渐近相位和振幅
Asymptotic phase and amplitude for classical and semiclassical stochastic oscillators via Koopman operator theory
摘要：
渐近相位是分析确定性极限环振子的一个基本量，随机振子的渐近相位也被提出了广义定义。在这篇文章中，我们表明，渐近相位和振幅也可以定义为经典和半经典随机振子在一个自然的和统一的方式，通过使用系统的Koopman算子的本征函数。我们表明，所提出的定义给出了适当的值的相位和振幅的强随机极限环振荡器，可激发系统进行噪声诱导的振荡，也为量子极限环振荡器在半经典制度。
英文摘要：
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.
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