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

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.

10 pages, 4 figures

References in corpus (6)

• Continuous Opinion Dynamics under Bounded Confidence: A Survey
• Exact Results for the Kuramoto Model with a Bimodal Frequency Distribution
• A stabilization theorem for dynamics of continuous opinions
• Algebraic Geometrization of the Kuramoto Model: Equilibria and Stability Analysis
• The Size of the Sync Basin Revisited
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Cited by in corpus (1)

• On the Robustness of Democratic Electoral Processes to Computational Propaganda