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- W2949274490 abstract "The Kuramoto model on networks over the circle is multistable, but its extension to the sphere synchronizes from almost all initial conditions. This result is unexpected and demands an explanation. We study two high-dimensional generalizations of the of the Kuramoto model on networks, where the oscillators evolve on a Riemannian manifold. Both systems are gradient descent flows of quadratic disagreement functions; we refer to them as geodesic and chordal consensus. For networks consisting of a single cycle, the Kuramoto model has an equilibrium set consisting of so-called splay states where the phases are equally spaced on the circle. For the geodesic consensus algorithm, we introduce a generalization of the splay states and show that they, as a set, are asymptotically stable. For both geodesic and chordal consensus, we show that if the Riemannian manifold is multiply connected, then the system is multistable. This explains the difference between the Kuramoto model on the circle and the sphere; the circle is multiply connected whereas the sphere is simply connected. To further illustrate the usefulness of these results we apply them to model synchronization in flocks of birds and aggregation in the social amoeba Dictyostelium discoideum." @default.
- W2949274490 created "2019-06-27" @default.
- W2949274490 creator A5017253285 @default.
- W2949274490 date "2019-06-18" @default.
- W2949274490 modified "2023-09-27" @default.
- W2949274490 title "Kuramoto models on Riemannian manifolds: Multiply connected implies multistable" @default.
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