Dynamics of Coupled Oscillator Systems - Abstract
A typical problem in data analysis is to eliminate a particular component of a given time series, e.g. to remove noise, trend, oscillation in a certain frequency band, etc. A whole variety of techniques has been designed to tackle this task by means of filtering in the frequency domain, smoothing in a running window, subtracting a fitted polynomial, and soon. Furthermore, a number of modern methods - principal mode decomposition, independent mode decomposition, empirical mode decomposition - represent a signal of interest as a sum of modes such that (at least) dominating modes are assumed to represent certain dynamical processes. Correspondingly, some of these modes can be analyzed separately or, on the contrary, if they are considered as irrelevant, they can be subtracted from the original data, so that the cleansed signal is processed. Here we elaborate on a technique, designed for analysis of signals, generated by coupled oscillatory systems. The technique is based on reconstruction of phase dynamics of the analyzed unit. The obtained equation is then used for generation of new, cleansed, data by excluding one, or, generally, several inputs to the system. For example, if only the deterministic part of the model is used, i.e. the noise term is omitted, then the simulated data represents the dynamics of noise-free system. This disentanglement procedure is neither the standard filtering (because the preserved and eliminated components can overlap in frequency domain) nor the mode decomposition (because the sum of preserved and eliminated components does not yield the original signal). Here we consider application of this approach to analysis of cardio-respiratory interaction in humans.