Fisher information and criticality in the Kuramoto model of nonidentical oscillators
Abstract
We use the Fisher information to provide a lens on the transition to synchronization of the Kuramoto model of nonidentical frequencies on a variety of undirected graphs. We numerically solve the equations of motion for a N =400 complete graph and N =1000 small-world, scale-free, uniform random, and random regular graphs. For large but finite graphs of small average diameter the Fisher information F as a function of coupling shows a peak closely coinciding with the critical point as determined by Kuramoto's order parameter or synchronization measure r . However, for graphs of larger average diameter the position of the peak in F differs from the critical point determined by estimates of r . On the one hand, this is a finite-size effect even at N =1000 ; however, we show across a range of topologies that the Fisher information peak points to a transition for smaller graphs that indicates structural changes in the numbers of locally phase-synchronized clusters, often directly from metastable to stable frequency synchronization. Solving explicitly for a two-cluster ansatz subject to Gaussian noise shows that the Fisher infomation peaks at such a transition. We discuss the implications for Fisher information as an indicator for edge-of-chaos phenomena in finite-coupled oscillator systems.
- Publication:
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Physical Review E
- Pub Date:
- August 2018
- DOI:
- 10.1103/PhysRevE.98.022302
- Bibcode:
- 2018PhRvE..98b2302K