Chronotaxicity and Dynamic Stability: From Theory to Quantitative Measures

Living systems operate far from equilibrium under continuous time-varying forcing across multiple temporal and spatial scales. From neural and cardiovascular rhythms to microcirculatory dynamics and circadian cycles, physiological processes are inherently nonautonomous. Classical stability concepts based on autonomous attractors and stationary limit cycles are therefore insufficient to explain how such systems remain robust yet adaptable.
In this talk, I will introduce chronotaxicity as a framework for nonautonomous oscillatory systems possessing time-dependent point attractors and contraction regions. Chronotaxic systems maintain stability under continuous forcing, providing a rigorous theoretical description of dynamic robustness.
To illustrate the generality of this concept, I will show how chronotaxicity can be observed in a controlled physical experiment. I will then present a new order parameter based on angular velocity for quantifying phase dynamics in numerical simulations of coupled nonautonomous oscillators, along with the methods collected in the Multiscale Oscillatory Dynamics Analysis (MODA) toolbox for analysing time-dependent oscillatory behaviour.
This approach provides a unified perspective on dynamic stability in complex systems, highlighting how living systems remain robust yet adaptable and suggesting quantitative signatures of dysfunction in health and disease. While the focus is on physiological and numerical models, it is broadly applicable to complex nonautonomous systems, underscoring its generality as a dynamical principle.