Chimeras unfolded
Georgi S. Medvedev, Matthew S. Mizuhara

TL;DR
This paper investigates the bifurcation mechanisms behind the emergence of complex spatiotemporal patterns, including chimeras, in the Kuramoto model, using stability analysis and Penrose diagrams to predict and analyze these phenomena.
Contribution
It introduces a codimension-2 bifurcation framework that explains the formation of chimeras and clusters, extending classical synchronization theory with new analytical tools.
Findings
Identification of various stable and traveling coherent structures.
Prediction of basins of existence for different patterns.
Demonstration of network topology effects on chimera organization.
Abstract
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. The linear stability analysis is used to estimate of the velocity distribution within these structures. Penrose diagrams, on the…
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