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Chimeras Unfolded
Journal article   Open access   Peer reviewed

Chimeras Unfolded

Georgi S. Medvedev and Matthew S. Mizuhara
Journal of statistical physics, v 186(3)
2022
DOI: https://doi.org/10.1007/s10955-022-02881-y
url
https://arxiv.org/abs/2105.07541View
SubmittedOpen Access (License Unspecified),  Open

Abstract

Article Mathematical and Computational Physics Physical Chemistry Physics Physics and Astronomy Quantum Physics Statistical Physics and Dynamical Systems Theoretical
The instability of mixing in the Kuramoto model of coupled phase oscillators is the key to understanding a range of spatiotemporal patterns, which feature prominently in collective dynamics of systems ranging from neuronal networks, to coupled lasers, to power grids. In this paper, we describe a codimension–2 bifurcation of mixing whose unfolding, in addition to the classical scenario of the onset of synchronization, also explains the formation of clusters and chimeras. We use a combination of linear stability analysis and Penrose diagrams to identify and analyze a variety of spatiotemporal patterns including stationary and traveling coherent clusters and twisted states, as well as their combinations with regions of incoherent behavior called chimera states. Penrose diagrams are used to locate the bifurcation of mixing and to determine its type. The linear stability analysis, on the other hand, yields the velocity distribution of the pattern emerging from the bifurcation. Furthermore, we show that network topology can endow chimera states with nontrivial spatial organization. In particular, we present twisted chimera states, whose coherent regions are organized as stationary or traveling twisted states. The analytical results are illustrated with numerical bifurcation diagrams computed for the Kuramoto model with uni-, bi-, and trimodal frequency distributions and all-to-all and nonlocal nearest-neighbor connectivity.

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4 citations in Web of Science
3 citations in Scopus

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Collaboration types
Domestic collaboration
Web of Science research areas
Physics, Mathematical
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