Phase Oscillator Network Models of Brain Dynamics

Laing, Carlo R.

doi:10.1002/9781119159193.ch37

Cited by 25 publications

(22 citation statements)

References 48 publications

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“…Another extension involves investigating a pair of populations of neurons, one excitatory and one inhibitory [ 41 ]. Coupling these may result in a PING rhythm [ 48 ], and if neurons are identical within each population, the coupled network may show interesting dynamics.…”

Section: Discussionmentioning

confidence: 99%

The Dynamics of Networks of Identical Theta Neurons

Laing

2018

J. Math. Neurosc.

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We consider finite and infinite all-to-all coupled networks of identical theta neurons. Two types of synaptic interactions are investigated: instantaneous and delayed (via first-order synaptic processing). Extensive use is made of the Watanabe/Strogatz (WS) ansatz for reducing the dimension of networks of identical sinusoidally-coupled oscillators. As well as the degeneracy associated with the constants of motion of the WS ansatz, we also find continuous families of solutions for instantaneously coupled neurons, resulting from the reversibility of the reduced model and the form of the synaptic input. We also investigate a number of similar related models. We conclude that the dynamics of networks of all-to-all coupled identical neurons can be surprisingly complicated.

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Section: Discussionmentioning

confidence: 99%

The Dynamics of Networks of Identical Theta Neurons

Laing

2018

J. Math. Neurosc.

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“…PING and ING oscillation mechanisms have been qualitatively reproduced by employing heuristic neural mass models (Wilson and Cowan, 1972;Gerstner et al, 2014). However, these standard firing rate models do not properly describe the synchronization and desynchronizaton phenomena occurring in neural populations (Devalle et al, 2017;Laing, 2017;Coombes and Byrne, 2019). Recently a new generation of neural mass models has been designed, which are able to exactly reproduce the network dynamics of spiking neurons of class I, for any degree of synchronization among the neurons (Luke et al, 2013;Laing, 2014;So et al, 2014;Montbrió et al, 2015).…”

Section: Introductionmentioning

confidence: 99%

Theta-Nested Gamma Oscillations in Next Generation Neural Mass Models

Segneri

Olmi

et al. 2020

Front. Comput. Neurosci.

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Theta-nested gamma oscillations have been reported in many areas of the brain and are believed to represent a fundamental mechanism to transfer information across spatial and temporal scales. In a series of recent experiments in vitro it has been possible to replicate with an optogenetic theta frequency stimulation several features of cross-frequency coupling (CFC) among theta and gamma rhythms observed in behaving animals. In order to reproduce the main findings of these experiments we have considered a new class of neural mass models able to reproduce exactly the macroscopic dynamics of spiking neural networks. In this framework, we have examined two setups able to support collective gamma oscillations: namely, the pyramidal interneuronal network gamma (PING) and the interneuronal network gamma (ING). In both setups we observe the emergence of theta-nested gamma oscillations by driving the system with a sinusoidal theta-forcing in proximity of a Hopf bifurcation. These mixed rhythms always display phase amplitude coupling. However, two different types of nested oscillations can be identified: one characterized by a perfect phase locking between theta and gamma rhythms, corresponding to an overall periodic behavior; another one where the locking is imperfect and the dynamics is quasi-periodic or even chaotic. From our analysis it emerges that the locked states are more frequent in the ING setup. In agreement with the experiments, we find theta-nested gamma oscillations for forcing frequencies in the range [1:10] Hz, whose amplitudes grow proportionally to the forcing intensity and which are clearly modulated by the theta phase. Furthermore, analogously to the experiments, the gamma power and the frequency of the gamma-power peak increase with the forcing amplitude. At variance with experimental findings, the gamma-power peak does not shift to higher frequencies by increasing the theta frequency. This effect can be obtained, in our model, only by incrementing, at the same time, also the stimulation power. An effect achieved by increasing the amplitude either of the noise or of the forcing term proportionally to the theta frequency. On the basis of our analysis both the PING and the ING mechanism give rise to theta-nested gamma oscillations with almost identical features.

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“…The ideas proposed by Ott and Antonsen were successfully applied to study the N→∞ limit in different kinds of networks of coupled units [16][17][18][19][20][21]. In cases where the composing elements of the system are excitable, such as neurons, an order parameter describing the synchrony of the network can indicate a highly synchronous state either because the units are spiking in phase, or because the units are quiescent near each other [22].…”

Section: Introductionmentioning

confidence: 99%

Observable for a Large System of Globally Coupled Excitable Units

Boari

Uribarri

Amador

et al. 2019

MCA

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The study of large arrays of coupled excitable systems has largely benefited from a technique proposed by Ott and Antonsen, which results in a low dimensional system of equations for the system’s order parameter. In this work, we show how to explicitly introduce a variable describing the global synaptic activation of the network into these family of models. This global variable is built by adding realistic synaptic time traces. We propose that this variable can, under certain conditions, be a good proxy for the local field potential of the network. We report experimental, in vivo, electrophysiology data supporting this claim.

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Phase Oscillator Network Models of Brain Dynamics

Cited by 25 publications

References 48 publications

The Dynamics of Networks of Identical Theta Neurons

The Dynamics of Networks of Identical Theta Neurons

Theta-Nested Gamma Oscillations in Next Generation Neural Mass Models

Observable for a Large System of Globally Coupled Excitable Units

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