Dynamics of Structured Networks of Winfree Oscillators

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Date
2021-02-10
Open Access Location
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Publisher
Frontiers Media SA
Rights
(c) 2021 The Author/s
CC BY
Abstract
Winfree oscillators are phase oscillator models of neurons, characterized by their phase response curve and pulsatile interaction function. We use the Ott/Antonsen ansatz to study large heterogeneous networks of Winfree oscillators, deriving low-dimensional differential equations which describe the evolution of the expected state of networks of oscillators. We consider the effects of correlations between an oscillator's in-degree and out-degree, and between the in- and out-degrees of an “upstream” and a “downstream” oscillator (degree assortativity). We also consider correlated heterogeneity, where some property of an oscillator is correlated with a structural property such as degree. We finally consider networks with parameter assortativity, coupling oscillators according to their intrinsic frequencies. The results show how different types of network structure influence its overall dynamics.
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Keywords
Ott/Antonsen, Winfree oscillators, assortativity, copula, coupled oscillators, degree, neuronal networks
Citation
Laing CR, Bläsche C, Means S. (2021). Dynamics of Structured Networks of Winfree Oscillators.. Front Syst Neurosci. 15. (pp. 631377-).
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