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  • Suprunenko(2014)3

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Generalized chronotaxic systems: time-dependent oscillatory dynamics stable under continuous perturbation

Research output: Contribution to journal › Journal article

Published
Article number032921
<mark>Journal publication date</mark>26/09/2014
<mark>Journal</mark>Physical Review E
Issue number3
Volume90
Number of pages10
Publication statusPublished
Original languageEnglish

Abstract

Chronotaxic systems represent deterministic nonautonomous oscillatory systems which are capable of resisting continuous external perturbations while having a complex time-dependent dynamics. Until their recent introduction in Phys. Rev. Lett. 111, 024101 (2013) chronotaxic systems had often been treated as stochastic, inappropriately, and the deterministic component had been ignored.
While the previous work addressed the case of the decoupled amplitude and phase dynamics, in this paper we develop a generalized theory of chronotaxic systems where such decoupling is not required. The theory presented is based on the concept of a time-dependent point attractor or a driven steady state and on the contraction theory of dynamical systems. This simplifies the analysis of
chronotaxic systems and makes possible the identification of chronotaxic systems with time-varying parameters. All types of chronotaxic dynamics are classified and their properties are discussed using the nonautonomous Poincaré oscillator as an example. We demonstrate that these types differ in their transient dynamics towards a driven steady state and according to their response to external
perturbations. Various possible realizations of chronotaxic systems are discussed, including systems with temporal chronotaxicity and interacting chronotaxic systems.

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Published by the American Physical Society under the terms of the Creative Commons Attribution 3.0 License. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI. Published by the American Physical Society