Chapter 1
Introduction
Peter V. E. McClintock and Aneta Stefanovska
Abstract To set the subject of book in context, a short discussion of oscillatory
dynamical systems with non-constant frequencies is provided. Such oscillators are
widespread, especially (but not only) in biology. It is pointed out that they can be
considered as thermodynamically open (physics) or non-autonomous (mathematics).
The difficulty of treating and analysing data derived from such systems is that most
earlier work, and most of the well-established methods, refer to dynamics where
the natural frequencies remain constant. Recent progress is discussed in five sections
corresponding to Parts of the book. They cover respectively theory, model-driven and
data-driven approaches, biological oscillators, applications, and the future. Ways of
using the book are suggested.
There are numerous oscillatory systems that are not periodic. In striking contrast to the
simple pendulum, which so often introduces the physics student to oscillation theory,
their characteristic frequencies vary in time. Such oscillators are found universally in
biology, and they also appear in other contexts too. Understanding their dynamics is
challenging, not least because physicists new to the area must be willing to discard,
or modify, many cherished notions dating back to their schooldays.
The problem is non-trivial, because in practice the origin of the time variability is often unknown (unlike e.g. heart-rate variability where respiration modulates
the heart rhythm, or the diurnal rhythm). In mathematical terms, the oscillations
are non-autonomous, reflecting the physics of open systems where the function of
each oscillator is affected by its environment. Time-frequency analysis is essential.
Recent approaches, including wavelet phase coherence analysis and nonlinear mode
decomposition, were described during the Workshop and form parts of several of
P. V. E. McClintock (B) · A. Stefanovska
Department of Physics, Lancaster University, LA1 4YB Lancaster, UK
e-mail: p.v.e.mcclintock@lancaster.ac.uk
A. Stefanovska
e-mail: aneta@lancaster.ac.uk
© Springer Nature Switzerland AG 2021
A. Stefanovska and P. V. E. McClintock (eds.), Physics of Biological
Oscillators, Understanding Complex Systems,
https://doi.org/10.1007/978-3-030-59805-1_1
1
Introduction
Peter V. E. McClintock and Aneta Stefanovska
Abstract To set the subject of book in context, a short discussion of oscillatory
dynamical systems with non-constant frequencies is provided. Such oscillators are
widespread, especially (but not only) in biology. It is pointed out that they can be
considered as thermodynamically open (physics) or non-autonomous (mathematics).
The difficulty of treating and analysing data derived from such systems is that most
earlier work, and most of the well-established methods, refer to dynamics where
the natural frequencies remain constant. Recent progress is discussed in five sections
corresponding to Parts of the book. They cover respectively theory, model-driven and
data-driven approaches, biological oscillators, applications, and the future. Ways of
using the book are suggested.
There are numerous oscillatory systems that are not periodic. In striking contrast to the
simple pendulum, which so often introduces the physics student to oscillation theory,
their characteristic frequencies vary in time. Such oscillators are found universally in
biology, and they also appear in other contexts too. Understanding their dynamics is
challenging, not least because physicists new to the area must be willing to discard,
or modify, many cherished notions dating back to their schooldays.
The problem is non-trivial, because in practice the origin of the time variability is often unknown (unlike e.g. heart-rate variability where respiration modulates
the heart rhythm, or the diurnal rhythm). In mathematical terms, the oscillations
are non-autonomous, reflecting the physics of open systems where the function of
each oscillator is affected by its environment. Time-frequency analysis is essential.
Recent approaches, including wavelet phase coherence analysis and nonlinear mode
decomposition, were described during the Workshop and form parts of several of
P. V. E. McClintock (B) · A. Stefanovska
Department of Physics, Lancaster University, LA1 4YB Lancaster, UK
e-mail: p.v.e.mcclintock@lancaster.ac.uk
A. Stefanovska
e-mail: aneta@lancaster.ac.uk
© Springer Nature Switzerland AG 2021
A. Stefanovska and P. V. E. McClintock (eds.), Physics of Biological
Oscillators, Understanding Complex Systems,
https://doi.org/10.1007/978-3-030-59805-1_1
1