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

Abstract

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.

Modelling chronotaxicity of cellular energy metabolism to facilitate the identification of altered metabolic states

“…1a . It was previously demonstrated that at least 30 cycles of oscillation are required to test for chronotaxicity 41 , therefore all cells which did not meet this requirement were excluded. 16 cells met this criteria.…”

“…In order to reliably test for chronotaxicity, it should be noted that the time series should be sufficiently long, i.e. contain at least 30 cycles of oscillation (may vary depending on the characteristics of the data), be evenly sampled, and have a sampling frequency which is high enough to capture the dynamics at the frequency of interest 41 .…”

Reconstructing Time-Dependent Dynamics

“…of chronotaxicity and their application to real data [33], [34]. This provides a framework in which experimentally observed fluctuations, which may previously have been regarded as noise, or arising from chaotic dynamics, may actually be considered as systems with underlying elements of determinism.…”

“…theory by combining it with the theory of nonautonomous systems [30] to provide a mechanism for stable oscillations with time-varying frequencies [31], [32]. A new framework of analysis has since been developed to detect such chronotaxic behavior [33], [34].…”

Time-varying coupling functions: Dynamical inference and cause of synchronization transitions

“…Very often these interactions are assessed successfully to a relatively great extend when they are considered isolated, however in some cases there is additional complexity due to external influences and the existing time-variability. From the aspect of mathematical models, such systems and their interactions are studied as non-autonomous dynamical systems [5][6][7][8][9]. The timevariability can have different effects on the interactions, including for example, changes in frequency, emergence or disappearance of connectivity, transitions to or out of qualitative states, or time-varying form of the coupling functions.…”