Spatio-temporal dynamics of chronotaxic systems
Early Stage Researcher: Maxime Lucas
Principle Investigators: Aneta Stefanovska (Lancaster, ULANC – major institution) and Duccio Fanelli (Florence, UF – partner institution)
Although Erwin Schrödinger in his 1944 book What Is Life? postulated that the life cannot be treated but within the framework of thermodynamically open systems and despite the extended progress ever since we still do not have a comprehensive theory of open systems. As they continuously exchange energy and matter with the environment, they are inevitably characteristsed by a time-variable dynamics. When oscillatory, they are characterized with time-variable characteristic frequencies.
It can now be appreciated that such systems abound in nature – spanning across physical systems, such as surface state electrons on liquid helium, solid state physics, quantum critical systems, astrophysics, and space science; and across living systems, from mitochondrial oscillations to the waves in the electrical activity of the brain; and across climate, ecology and sociological networks.
The group in Lancaster has recently proposed a theory of such systems and named them chronotaxic (from chronos – time and taxis – order). In mathematical terms they belong to the class of non-autonomous systems and are characterized by a point attractor. They are related to systems with hyperbolic trajectories and to phase-locked systems. To date the theory of chronotaxic systems was restricted only to temporal dynamics.
The goal of the project is to develop new theories for spatio-temporal dynamics of chronotaxic systems, including investigations of effects of delays and networks of time-dependent oscillatory systems.
The project will combine theoretical and numerical approaches as well as practical applications. It will include the study of real data based on the large library of biological data related to the cellular and systemic level – including cardiovascular and brain dynamics – available at Lancaster. There will be opportunities to investigate the spatio-temporal dynamics of chronotaxic systems under experimental conditions in collaboration with the Lancaster Quantum Technology Centre where experimental models of chronotaxic systems will be created using optical microresonators.
- E Schrödinger, What Is Life? & Mind and Matter. Cambridge University Press, 1974 ISBN 0-521-09397-X.
- YF Suprunenko, PT Clemson, A Stefanovska: Chronotaxic systems: A new class of self-sustained nonautonomous oscillators, Phys Rev Lett 111: 024101, 2013
- YF Suprunenko, PT Clemson, A Stefanovska: Chronotaxic systems with separable amplitude and phase dynamics, Phys Rev E 89: 012922, 2014
- PT Clemson, YF Suprunenko, T Stankovski, A Stefanovska: Inverse approach to chronotaxic systems for single-variable time series, Phys Rev E 89: 032904, 2014
- YF Suprunenko, A Stefanovska: Generalized chronotaxic systems: Time-dependent oscillatory dynamics stable under continuous perturbation, Phys Rev E 90: 032921, 2014
- PT Clemson, A Stefanovska: Discerning non-autonomous dynamics, Phys Rep 542: 297-368, 2014