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.
Highlights
The theory of nonautonomous dynamical systems has increasingly been recognised as a necessity in the treatment of the inherent time-variability of biological systems [1]
Phase fluctuation analysis provides a measure of statistical effects observed in a signal, whilst the dynamical Bayesian inference method infers a model of differential equations and gives a measure of dynamical mechanisms, i.e., the evaluation of chronotaxicity relies on the inferred parameters of the model
The recent formulation of chronotaxic systems provides a completely novel approach to the characterisation of time-varying dynamics in real data. They provide a framework in which systems may be time-varying, both in terms of their amplitude and phase dynamics, continuously perturbed, and yet still exhibit determinism
Summary
The theory of nonautonomous dynamical systems has increasingly been recognised as a necessity in the treatment of the inherent time-variability of biological systems [1]. The complexity observed in biological systems has led to attempts to treat them with chaos theory [3], this does not allow for the apparent stability of these systems, irrespective of their initial conditions Such characteristics of biological oscillators suggests underlying determinism or control of both their amplitudes and frequencies, even with continuous perturbations. The inherent time-variability of the frequency of the dynamics arising from a chronotaxic system means that it cannot be accurately characterized by any method based on averaging This novel class of systems requires new inverse approach methods, with the focus on the extraction and identification of the dynamics of the drive system, and its influence on the response system.
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