Comment on "Phase Reduction of Stochastic Limit Cycle Oscillators"
Comment on "Phase Reduction of Stochastic Limit Cycle Oscillators"
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对“随机极限环振荡器的相位减少”的评论
DOI：
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发表时间：
2008
期刊：
影响因子：
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通讯作者：
G. Ermentrout
中科院分区：
文献类型：
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作者：
H. Nakao;Jun;G. Ermentrout
Yoshimura和Arai [1]在最近的一封信中指出，[2，3，4]中所用的传统相位随机微分方程（ε）不能很好地逼近噪声驱动的极限环振荡器，并提出了一种修正的艾德相位微分方程。在这里，我们认为，他们的说法并不总是正确的;这两个随机微分方程是有效的，这取决于thesituation。由于物理噪声有一个相关的时间尺度和所有的振荡器有一个特征吸引率，这两个随机微分方程是适当的取决于这两个尺度的相对大小。作为一个简单的例子，让我们对[1，2]中使用的由Ornstein-Uhlenbeck过程（OUP）[5]产生的色噪声驱动的Stuart-Landau（SL）模型进行重新缩放，使得振幅弛豫时间显式出现，同时保持极限环及其等时线不变，W stec（t）= {T
In a recent Letter, Yoshimura and Arai [1] claimed that the conventional phase stochastic differential equation(SDE) used in [2, 3, 4] does not give a proper approximation to limit-cycle oscillators driven by noise, and proposeda modified phase SDE. Here we argue that their claim is not always correct; both SDEs are valid depending on thesituation.Since physical noise has an associated time scale and all oscillators have a characteristic rate of attraction, whichof the two SDEs is appropriate depends on the relative sizes of these two scales. As a simple example, let us considerthe Stuart-Landau (SL) model used in [1, 2] driven by a colored noise generated by the Ornstein-Uhlenbeck process(OUP) [5], which is rescaled such that the amplitude relaxation time explicitly appears while keeping the limit cycleand its isochrons invariant,W˙ (t) = {T