Janson N B, Balanov A G, Anishchenko V S, McClintock P V E
Department of Physics, Lancaster University, Lancaster, LA1 4YB, United Kingdom.
Phys Rev E Stat Nonlin Soft Matter Phys. 2002 Mar;65(3 Pt 2A):036211. doi: 10.1103/PhysRevE.65.036211. Epub 2002 Feb 15.
A general approach is developed for the detection of phase relationships between two or more different oscillatory processes interacting within a single system, using one-dimensional time series only. It is based on the introduction of angles and radii of return times maps, and on studying the dynamics of the angles. An explicit unique relationship is derived between angles and the conventional phase difference introduced earlier for bivariate data. It is valid under conditions of weak forcing. This correspondence is confirmed numerically for a nonstationary process in a forced Van der Pol system. A model describing the angles' behavior for a dynamical system under weak quasiperiodic forcing with an arbitrary number of independent frequencies is derived.
本文提出了一种通用方法，仅使用一维时间序列来检测在单个系统中相互作用的两个或多个不同振荡过程之间的相位关系。该方法基于引入返回时间映射的角度和半径，并研究角度的动力学。推导了角度与早期为二元数据引入的传统相位差之间明确的唯一关系。在弱强迫条件下该关系成立。通过数值验证了该对应关系适用于受迫范德波尔系统中的非平稳过程。推导了一个模型，用于描述在具有任意数量独立频率的弱准周期强迫下动态系统中角度的行为。
