Kralemann Björn, Cimponeriu Laura, Rosenblum Michael, Pikovsky Arkady, Mrowka Ralf
Department of Physics and Astronomy, University of Potsdam, Karl-Liebknecht Strasse 24-25, D-14476 Potsdam, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jun;77(6 Pt 2):066205. doi: 10.1103/PhysRevE.77.066205. Epub 2008 Jun 9.
We systematically develop a technique for reconstructing the phase dynamics equations for coupled oscillators from data. For autonomous oscillators and for two interacting oscillators we demonstrate how phase estimates obtained from general scalar observables can be transformed to genuine phases. This allows us to obtain an invariant description of the phase dynamics in terms of the genuine, observable-independent phases. We discuss the importance of this transformation for characterization of strength and directionality of interaction from bivariate data. Moreover, we demonstrate that natural (autonomous) frequencies of oscillators can be recovered if several observations of coupled systems at different, yet unknown coupling strengths are available. We illustrate our method by several numerical examples and apply it to a human electrocardiogram and to a physical experiment with coupled metronomes.
我们系统地开发了一种从数据重建耦合振子相位动力学方程的技术。对于自治振子和两个相互作用的振子，我们展示了如何将从一般标量可观测量获得的相位估计转换为真实相位。这使我们能够根据真实的、与可观测量无关的相位获得相位动力学的不变描述。我们讨论了这种变换对于从二元数据表征相互作用强度和方向性的重要性。此外，我们证明，如果有耦合系统在不同但未知耦合强度下的多个观测值，就可以恢复振子的自然（自治）频率。我们通过几个数值例子说明了我们的方法，并将其应用于人体心电图和耦合节拍器的物理实验。
