Presentation Information
[SS14-01]Between deterministic and stochastic dynamics: Coupled multiscale oscillatory systems
*Aneta Stefanovska1 (1. Physics Department, Lancaster University, Lancaster (UK))
Keywords:
time-series analyses,coupled oscillatory systems,multiscale dynamics,non-autonomous dynamics,time-localised dynamics,biological oscillators
We still do not have a working theory for multiscale coupled oscillatory systems. This is despite many studies indicating that the interactions in living systems are usually via frequency/phase couplings such as the well-known modulation of heart rate by breathing known as respiratory sinus arrhythmia. Moreover, when we discuss stationarities, we mainly consider amplitude fluctuations over time.
For either an autonomous dynamical system with a time-independent vector field, or a nonautonomous dynamical system with a time-dependent vector field, dynamics is traditionally analysed in terms of the behaviour as time goes to infinity. For example, attractors, repellers, asymptotic stability, and Lyapunov exponents are typically defined in terms of such long-time-asymptotic behaviour. In this talk we will introduce a new class of dynamical systems, named chronotaxic (from chronos - time and taxis – order), that maintain stability when their frequencies/phases are perturbed [1]. This class of systems requires an approach based on finite-timescales rather than the indefinite-timescales on which deterministic or stochastic models are conventionally treated.
When analysing their properties from recorded time-series we must bear in mind the need for finite-timescales. This inevitably leads to consideration of the Heisenberg uncertainty principle and the need to optimise between frequency-resolution and time-localisation. We will revise current methods and illustrate that a seeming disorder may unwind as highly ordered multiscale dynamics if appropriate methods for multiscale finite-time dynamics are considered [2].
Finally, we will illustrate the benefits of this approach based on our recent study of the circadian rhythm [3]. We reveal its time-varying nature, and its further changes in the absence of clock genes and following administration of methamphetamine. Disruptions to the circadian rhythm in mammals is associated with alterations in their physiological and mental states, hence our new insights may have profound implications for health and disease.
[1] Suprunenko, Y.F., Clemson, P. T., Stefanovska, A. (2013). Phys. Rev. Lett. 111: 024101.
[2] Rowland Adams, J., Newman, J., Stefanovska, A. (2023). Eur. Phys. J.: Spec. Top. 232: 3435-3457.
[3] Barnes, S. J. K., Alanazi, M., Yamazaki, S., Stefanovska, A. (2025). PNAS Nexus, 4: pgaf070.
For either an autonomous dynamical system with a time-independent vector field, or a nonautonomous dynamical system with a time-dependent vector field, dynamics is traditionally analysed in terms of the behaviour as time goes to infinity. For example, attractors, repellers, asymptotic stability, and Lyapunov exponents are typically defined in terms of such long-time-asymptotic behaviour. In this talk we will introduce a new class of dynamical systems, named chronotaxic (from chronos - time and taxis – order), that maintain stability when their frequencies/phases are perturbed [1]. This class of systems requires an approach based on finite-timescales rather than the indefinite-timescales on which deterministic or stochastic models are conventionally treated.
When analysing their properties from recorded time-series we must bear in mind the need for finite-timescales. This inevitably leads to consideration of the Heisenberg uncertainty principle and the need to optimise between frequency-resolution and time-localisation. We will revise current methods and illustrate that a seeming disorder may unwind as highly ordered multiscale dynamics if appropriate methods for multiscale finite-time dynamics are considered [2].
Finally, we will illustrate the benefits of this approach based on our recent study of the circadian rhythm [3]. We reveal its time-varying nature, and its further changes in the absence of clock genes and following administration of methamphetamine. Disruptions to the circadian rhythm in mammals is associated with alterations in their physiological and mental states, hence our new insights may have profound implications for health and disease.
[1] Suprunenko, Y.F., Clemson, P. T., Stefanovska, A. (2013). Phys. Rev. Lett. 111: 024101.
[2] Rowland Adams, J., Newman, J., Stefanovska, A. (2023). Eur. Phys. J.: Spec. Top. 232: 3435-3457.
[3] Barnes, S. J. K., Alanazi, M., Yamazaki, S., Stefanovska, A. (2025). PNAS Nexus, 4: pgaf070.