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Journal article
A global bifurcation organizing rhythmic activity in a coupled network
Chaos (Woodbury, N.Y.), v 32(8), 083116
01 Aug 2022
PMID: 36049909
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.
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Details
- Title
- A global bifurcation organizing rhythmic activity in a coupled network
- Creators
- Georgi S. Medvedev - Drexel University, MathematicsMatthew S. Mizuhara - College of New JerseyAndrew Phillips - Drexel University
- Publication Details
- Chaos (Woodbury, N.Y.), v 32(8), 083116
- Publisher
- AIP Publishing
- Number of pages
- 13
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:000874821400001
- Scopus ID
- 2-s2.0-85136993558
- Other Identifier
- 991021861292804721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical