A global bifurcation organizing rhythmic activity in a coupled network

Author:

Medvedev Georgi S.1ORCID,Mizuhara Matthew S.2ORCID,Phillips Andrew3

Affiliation:

1. Department of Mathematics, Drexel University, Philadelphia, Pennsylvania 19104, USA

2. Department of Mathematics and Statistics, The College of New Jersey, Ewing, New Jersey 08628, USA

3. Department of Physics, Drexel University, Philadelphia, Pennsylvania 19104, USA

Abstract

We study a system of coupled phase oscillators near a saddle-node on 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 Ott–Antonsen reduction and geometric techniques for ordinary differential equations, we identify heteroclinic bifurcation in a family of vector fields on a cylinder, which explains the change in collective dynamics. Specifically, we show that heteroclinic bifurcation separates two topologically distinct families of limit cycles: contractible limit cycles before bifurcation from noncontractibile ones after bifurcation. Both families are stable for the model at hand.

Funder

Division of Mathematical Sciences

The College of New Jersey

Publisher

AIP Publishing

Subject

Applied Mathematics,General Physics and Astronomy,Mathematical Physics,Statistical and Nonlinear Physics

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Social and nonlinear dynamics unite: musical group synchrony;Trends in Cognitive Sciences;2023-11

2. Introduction to Focus Issue: Dynamics of oscillator populations;Chaos: An Interdisciplinary Journal of Nonlinear Science;2023-01-01

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