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Preprint
Instability of mixing in the Kuramoto model: From bifurcations to patterns
arXiv.org
31 Aug 2020
Abstract
We study patterns observed right after the loss of stability of mixing in the
Kuramoto model of coupled phase oscillators with random intrinsic frequencies
on large graphs, which can also be random. We show that the emergent patterns
are formed via two independent mechanisms determined by the shape of the
frequency distribution and the limiting structure of the underlying graph
sequence. Specifically, we identify two nested eigenvalue problems whose
eigenvectors (unstable modes) determine the structure of the nascent patterns.
The analysis is illustrated with the results of the numerical experiments with
the Kuramoto model with unimodal and bimodal frequency distributions on certain
graphs.
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Details
- Title
- Instability of mixing in the Kuramoto model: From bifurcations to patterns
- Creators
- Hayato ChibaGeorgi S MedvedevMatthew S Mizuhara
- Publication Details
- arXiv.org
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021862732504721