Chavez Mario, Adam Claude, Navarro Vincent, Boccaletti Stefano, Martinerie Jacques
Laboratoire de Neurosciences Cognitives et Imagerie Cérébrale (LENA), CNRS UPR-640, Hôpital de la Salpêtrière, 47 Bd. de l'Hôpital, 75651 Paris Cedex 13, France.
Chaos. 2005 Jun;15(2):23904. doi: 10.1063/1.1938467.
We address the problem of detecting, from scalar observations, the time scales involved in synchronization of complex oscillators with several spectral components. Using a recent data-driven procedure for analyzing nonlinear and nonstationary signals [Huang, Proc. R. Soc. London A 454, 903 (1998)], we decompose a time series in distinct oscillation modes which may display a time varying spectrum. When applied to coupled oscillators with multiple time scales, we found that motions are captured in a finite number of phase-locked oscillations. Further, in the synchronized state distinct phenomena as phase slips, anti-phase or perfect phase locking can be simultaneously observed at specific time scales. This fully data-driven approach (without a priori choice of filters or basis functions) is tested on numerical examples and illustrated on electric intracranial signals recorded from an epileptic patient. Implications for the study of the build-up of synchronized states in nonstationary and noisy systems are pointed out.
我们研究了从标量观测中检测复杂振荡器同步中涉及的时间尺度的问题，这些复杂振荡器具有多个频谱分量。使用最近一种用于分析非线性和非平稳信号的数据驱动程序[黄，《英国皇家学会学报A》454, 903 (1998)]，我们将一个时间序列分解为不同的振荡模式，这些模式可能显示出随时间变化的频谱。当应用于具有多个时间尺度的耦合振荡器时，我们发现运动被捕获在有限数量的锁相振荡中。此外，在同步状态下，可以在特定时间尺度上同时观察到诸如相位滑移、反相或完美锁相等不同现象。这种完全数据驱动的方法（无需事先选择滤波器或基函数）在数值示例上进行了测试，并在从一名癫痫患者记录的颅内电信号上进行了说明。指出了其对研究非平稳和噪声系统中同步状态形成的意义。
