Abstract
Following the development of a new class of self-sustained oscillators with a time-varying but stable frequency, the inverse approach to these systems is now formulated. We show how observed data arranged in a single-variable time series can be used to recognize such systems. This approach makes use of time-frequency domain information using the wavelet transform as well as the recently developed method of Bayesian-based inference. In addition, a set of methods, named phase fluctuation analysis, is introduced to detect the defining properties of the new class of systems by directly analyzing the statistics of the observed perturbations.We apply these methods to numerical examples but also elaborate further on the cardiac system.
Highlights
A new class of oscillatory systems which are characterized by a time-varying but stable frequency has been recently developed [1]
Following Refs. [1,22], chronotaxic systems are defined as a subclass of nonautonomous dynamical systems, which means their dynamics is governed by an independent variable or time-dependent component
Following the brief introduction of chronotaxic systems we focus on tackling such systems in the inverse approach
Summary
A new class of oscillatory systems which are characterized by a time-varying but stable frequency has been recently developed [1]. Methods to fit nonautonomous models to data have been investigated [12], including a novel technique based on Bayesian inference [13,14] which is able to track time-dependent system parameters [15,16]. These methods have been successfully applied to many areas including blood flow dynamics [17,18], aging [19,20], neuroscience [21], and climate science [8].
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