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arXiv · 2007.01214

Clusterization and phase diagram of the bimodal Kuramoto model with bounded confidence

André Reggio·Robin Delabays·Philippe Jacquod
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Abstract

Inspired by the Deffuant and Hegselmann-Krause models of opinion dynamics, we extend the Kuramoto model to account for confidence bounds, i.e., vanishing interactions between pairs of oscillators when their phases differ by more than a certain value. We focus on Kuramoto oscillators with peaked, bimodal distribution of natural frequencies. We show that, in this case, the fixed-points for the extended model are made of certain numbers of independent clusters of oscillators, depending on the length of the confidence bound -- the interaction range -- and the distance between the two peaks of the bimodal distribution of natural frequencies. This allows us to construct the phase diagram of attractive fixed-points for the bimodal Kuramoto model with bounded confidence and to analytically explain clusterization in dynamical systems with bounded confidence.

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André Reggio, Robin Delabays, Philippe Jacquod. 2020-06-30. Clusterization and phase diagram of the bimodal Kuramoto model with bounded confidence. https://doi.org/10.1063/5.0020436

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