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What information can be extracted from the recordings of physiological oscillations and their rhythms?

Biological systems (organisms, organs, cells, cellular organelles, etc.) can be studied experimentally by observing and recording the time series of characteristic quantities that describe the system. Examples of such quantities are: densities of chemical substances (glucose, oxygen, ATP and metabolites, etc.), cell membrane voltage potential, electrocardiogram, etc. Often such signals represent physiological oscillations with certain rhythms.

What information can be extracted from the recordings of physiological oscillations and their rhythms? The answer depends on the model of the system. The simplest models of physiological oscillations take into account only mean rhythms. However, it is known from observations that rhythms can speed up and slow down, leading to a remarkable feature of a biological system's dynamics – its time-variability. Such time-variability puzzled researchers for a long time. Often, time-variability of physiological oscillations is modelled as being fully stochastic. Alternatively, chaos theory provided a class of non-time-varying deterministic models to describe apparent time-variability in living systems. However, I will show that both of these classes of models (stochastic and chaotic) ignore an important feature of biological systems, leading to a loss of important information in the study.

In this talk, the main question stated in the title will be answered using the approach of non-autonomous dynamical systems, where the time-variability is taken into account explicitly. The resulting model of physiological oscillations is based on the notion of a time-varying set with contraction properties together with positively invariant subset. Theory and applications to the inverse approach problem in real life systems will be discussed. The application to a cardio-respiratory system will be discussed in detail.