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arXiv · 2203.01456

A global bifurcation organizing rhythmic activity in a coupled network

Georgi S. Medvedev·Matthew S. Mizuhara·Andrew Phillips
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Abstract

We study a system of coupled phase oscillators near a saddle-node on an invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the qualitative properties of collective dynamics. Using the Ott-Antonsen reduction and geometric techniques for ordinary differential equations, we identify a heteroclinic bifurcation in a family of vector fields on a cylinder, which explains the change in collective dynamics. Specifically, we show that the heteroclinic bifurcation separates two topologically distinct families of limit cycles: contractible limit cycles before the bifurcation from noncontractibile ones after the bifurcation. Both families are stable for the model at hand.

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Georgi S. Medvedev, Matthew S. Mizuhara, Andrew Phillips. 2022-03-02. A global bifurcation organizing rhythmic activity in a coupled network. https://doi.org/10.1063/5.0089946

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