论文标题
双峰库拉莫托模型的聚类和相图具有有限的置信度
Clusterization and phase diagram of the bimodal Kuramoto model with bounded confidence
论文作者
论文摘要
受舆论动力学模型的脱俗和赫格尔曼 - 夸隆模型的启发，我们扩展了库拉莫托模型，以说明置信度界限，即当它们的相位差异超过一定价值时，振荡器之间的相互作用消失了。我们专注于具有固有频率的峰值双峰分布的库拉莫托振荡器。我们表明，在这种情况下，扩展模型的固定点是由振荡器的一定数量的独立簇组成的，具体取决于置信度结合的长度 - 相互作用范围 - 相互作用范围 - 以及固有频率双峰分布的两个峰之间的距离。这使我们能够以有界的置信构建双峰库拉莫托模型的有吸引力的固定点的相图，并以有限的置信度分析动态系统中的聚类。
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.
