Asymptotic phase for stochastic oscillators.
Asymptotic phase for stochastic oscillators.
复制标题
随机振荡器的渐近阶段。
DOI：
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发表时间：
2014
影响因子：
8.6
通讯作者：
B. Lindner
中科院分区：
文献类型：
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作者：
P. Thomas;B. Lindner
振动和噪声在物理和生物系统中普遍存在。当振荡产生于确定性极限环时，夹带和同步可以用渐近相函数来分析。在存在噪声的情况下，渐近相位不再被很好地定义。我们引入了一个新的定义渐近相位的最慢衰减模式的Kolmogorov向后操作。我们的随机渐近相位是很好地定义的噪声振荡器，即使当振荡是噪声相关的。在噪声消失的极限下，它退化为经典的渐近相位。相位可以通过求解本征值问题或通过振荡密度接近其稳态的经验观察来获得。
Oscillations and noise are ubiquitous in physical and biological systems. When oscillations arise from a deterministic limit cycle, entrainment and synchronization may be analyzed in terms of the asymptotic phase function. In the presence of noise, the asymptotic phase is no longer well defined. We introduce a new definition of asymptotic phase in terms of the slowest decaying modes of the Kolmogorov backward operator. Our stochastic asymptotic phase is well defined for noisy oscillators, even when the oscillations are noise dependent. It reduces to the classical asymptotic phase in the limit of vanishing noise. The phase can be obtained either by solving an eigenvalue problem, or by empirical observation of an oscillating density's approach to its steady state.
影响因子：
8.6
作者：
Schwabedal, Justus T. C.;Pikovsky, Arkady
通讯作者：
Pikovsky, Arkady