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Explosive behaviour in networks of Winfree oscillators

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  • Means, Shawn
  • Laing, Carlo R.

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.

Suggested Citation

  • Means, Shawn & Laing, Carlo R., 2022. "Explosive behaviour in networks of Winfree oscillators," Chaos, Solitons & Fractals, Elsevier, vol. 160(C).
    • Handle: RePEc:eee:chsofr:v:160:y:2022:i:c:s0960077922004647
    DOI: 10.1016/j.chaos.2022.112254
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    References listed on IDEAS

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    1. Volker Pernice & Benjamin Staude & Stefano Cardanobile & Stefan Rotter, 2011. "How Structure Determines Correlations in Neuronal Networks," PLOS Computational Biology, Public Library of Science, vol. 7(5), pages 1-14, May.
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