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arXiv · 2211.15617

Information geometry and synchronization phase transition in Kuramoto model

Artem Alexandrov·Alexander Gorsky
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Abstract

We discuss the recently proposed description of Kuramoto model in terms of hyperbolic space and relate it to the information geometry. In particular the dynamical equation in Kuramoto all-to-all model is identified with the gradient flow of the Kullback-Leibner divergence on the statistical manifold. The Fisher information metric is evaluated for the Kuramoto and Kuramoto-Shakagichi models. We argue that the components of Fisher metric diverge at the critical point hence it can be used as an alternative order parameter for the synchronization phase transition.

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Artem Alexandrov, Alexander Gorsky. 2022-11-28. Information geometry and synchronization phase transition in Kuramoto model. https://doi.org/10.1103/physreve.107.044211

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