Chapter 3
Reduced Phase Models of Oscillatory
Neural Networks
Bastian Pietras and Andreas Daffertshofer
Abstract Phase reduction facilitates the analysis of networks of (weakly) coupled oscillators. Synchronization regions can be uncovered and also non-trivial network behavior can be foreseen via the reduced phase dynamics. Phase models have
become an essential tool for describing and analyzing rhythmic neural activity. It is
widely accepted that in oscillatory neural networks, phase synchronization is crucial
for information processing and information routing. Accurately deriving the phase
dynamics of interacting neural oscillators is far from trivial. We demonstrate how different reduction techniques of a network of interacting Wilson-Cowan neural masses
can lead to different dynamics of the reduced networks of phase oscillators. We pinpoint caveats and sensitive issues in the derivation of the phase dynamics and show
that an accurately derived phase model properly captures the collective dynamics.
We finally investigate the influence of strong interactions and biologically plausible
connectivity structures on the network behavior.
3.1 Introduction
Oscillatory behavior abounds across many different scales of the human brain
[17, 18, 80]. To trace and describe these neural oscillations, the development and
design of recording techniques and models have benefitted from mutual interaction
between experimental and theoretical neuroscientists. Still, linking recordings of
brain activity to the underlying neuronal mechanisms remains an urgent challenge.
A promising approach to model large-scale brain dynamics builds on networks of
B. Pietras (B)
Institute of Mathematics, Technische Universität Berlin & Bernstein Center
for Computational Neuroscience, Berlin, Germany
e-mail: pietras@tu-berlin.de
A. Daffertshofer
Faculty of Behavioural and Movement Sciences, Amsterdam Movement
Sciences & Institute for Brain and Behaviour Amsterdam, Vrije Universiteit Amsterdam,
Amsterdam, The Netherlands
e-mail: a.daffertshofer@vu.nl
© 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_3
29
Reduced Phase Models of Oscillatory
Neural Networks
Bastian Pietras and Andreas Daffertshofer
Abstract Phase reduction facilitates the analysis of networks of (weakly) coupled oscillators. Synchronization regions can be uncovered and also non-trivial network behavior can be foreseen via the reduced phase dynamics. Phase models have
become an essential tool for describing and analyzing rhythmic neural activity. It is
widely accepted that in oscillatory neural networks, phase synchronization is crucial
for information processing and information routing. Accurately deriving the phase
dynamics of interacting neural oscillators is far from trivial. We demonstrate how different reduction techniques of a network of interacting Wilson-Cowan neural masses
can lead to different dynamics of the reduced networks of phase oscillators. We pinpoint caveats and sensitive issues in the derivation of the phase dynamics and show
that an accurately derived phase model properly captures the collective dynamics.
We finally investigate the influence of strong interactions and biologically plausible
connectivity structures on the network behavior.
3.1 Introduction
Oscillatory behavior abounds across many different scales of the human brain
[17, 18, 80]. To trace and describe these neural oscillations, the development and
design of recording techniques and models have benefitted from mutual interaction
between experimental and theoretical neuroscientists. Still, linking recordings of
brain activity to the underlying neuronal mechanisms remains an urgent challenge.
A promising approach to model large-scale brain dynamics builds on networks of
B. Pietras (B)
Institute of Mathematics, Technische Universität Berlin & Bernstein Center
for Computational Neuroscience, Berlin, Germany
e-mail: pietras@tu-berlin.de
A. Daffertshofer
Faculty of Behavioural and Movement Sciences, Amsterdam Movement
Sciences & Institute for Brain and Behaviour Amsterdam, Vrije Universiteit Amsterdam,
Amsterdam, The Netherlands
e-mail: a.daffertshofer@vu.nl
© 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_3
29