Detecting Chronotaxic Systems from Single-Variable Time Series with Separable Amplitude and Phase

The recent introduction of chronotaxic systems provides the means to describe nonautonomous systems with stable yet time-varying frequencies which are resistant to continuous external perturbations. This approach facilitates realistic characterization of the oscillations observed in living systems, including the observation of transitions in dynamics which were not considered previously. The novelty of this approach necessitated the development of a new set of methods for the inference of the dynamics and interactions present in chronotaxic systems. These methods, based on Bayesian inference and detrended fluctuation analysis, can identify chronotaxicity in phase dynamics extracted from a single time series. Here, they are applied to numerical examples and real experimental electroencephalogram (EEG) data. We also review the current methods, including their assumptions and limitations, elaborate on their implementation, and discuss future perspectives.