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arXiv · 2205.10987

Explosive behaviour in networks of Winfree oscillators

Shawn Means·Carlo Laing
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Abstract

We consider directed networks of Winfree oscillators with power law distributed in- and out-degree distributions. Gaussian and power law distributed intrinsic frequencies are considered, and these frequencies are positively correlated with oscillators' in-degrees. The Ott/Antonsen ansatz is used to derive degree-based mean field equations for the expected dynamics of networks, and these are numerically analysed. In a variety of cases "explosive" transitions between either two different steady states or between a steady state and a periodic solution are found, and these transitions are explained using bifurcation theory.

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Shawn Means, Carlo Laing. 2022-05-23. Explosive behaviour in networks of Winfree oscillators. https://doi.org/10.1016/j.chaos.2022.112254

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