有界置信下双峰Kuramoto模型的离散化和phase diagram
Clusterization and phase diagram of the bimodal Kuramoto model with bounded confidence
摘要：
受观点动力学的Deffuant和Hegselmann-Krause模型的启发，我们扩展了Kuramoto模型来考虑置信区间，即，当成对的振荡器的相位相差超过一定值时，它们之间的相互作用消失。我们专注于仓本振荡器的峰值，双峰分布的固有频率。我们表明，在这种情况下，扩展模型的固定点是由一定数量的独立集群的振荡器，这取决于长度的置信区间-的相互作用范围-和固有频率的双峰分布的两个峰值之间的距离。这使我们能够构建有吸引力的不动点的相图的双峰仓本模型与有界的信心，并解析地解释集群在动力系统与有界的信心。
英文摘要：
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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