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Inspired by the Deffuant and Hegselmann-Krause models of opinion dynamics, weextend the Kuramoto model to account for confidence bounds, i.e., vanishinginteractions between pairs of oscillators when their phases differ by more thana certain value. We focus on Kuramoto oscillators with peaked, bimodaldistribution of natural frequencies. We show that, in this case, thefixed-points for the extended model are made of certain numbers of independentclusters of oscillators, depending on the length of the confidence bound -- theinteraction range -- and the distance between the two peaks of the bimodaldistribution of natural frequencies. This allows us to construct the phasediagram of attractive fixed-points for the bimodal Kuramoto model with boundedconfidence and to analytically explain clusterization in dynamical systems withbounded confidence.

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