论文标题
脉冲耦合振荡器簇动力学的渗透临界指数
Percolation critical exponents in cluster kinetics of pulse-coupled oscillators
论文作者
论文摘要
先前已经研究了导致脉冲耦合振荡器同步的瞬态动力学，作为同步簇的聚合过程，并且已经提出了群集大小分布的速率方程。但是，尚未解决一般簇大小的簇大小分布的演变。在本文中，我们从渗透模型的角度研究了簇大小分布的演变，这是将聚合数量作为附着键的数量的数量。具体而言，我们使用特征群集大小在渗透阈值从下面接近特征群集大小差异的属性的特定属性来得出群集大小分布的缩放形式。通过模拟，可以证实缩放形式很好地解释了群集大小分布的演变。基于分布行为，我们发现所有振荡器的巨大簇在阈值下不连续形成，并且在一维键渗透模型中不会发生进一步的聚集。最后，我们从爆炸性渗透模型中全局抑制的角度讨论了巨型簇的不连续形成的起源。为此，我们将聚合过程近似为群集 - 簇聚集，并具有给定的碰撞内核。我们认为，本文提出的理论方法可用于了解广泛的同步的瞬时动力学。
Transient dynamics leading to the synchrony of pulse-coupled oscillators has previously been studied as an aggregation process of synchronous clusters, and a rate equation for the cluster size distribution has been proposed. However, the evolution of the cluster size distribution for general cluster sizes has not been solved yet. In this paper, we study the evolution of the cluster size distribution from the perspective of a percolation model by regarding the number of aggregations as the number of attached bonds. Specifically, we derive the scaling form of the cluster size distribution with specific values of the critical exponents using the property that the characteristic cluster size diverges as the percolation threshold is approached from below. Through simulation, it is confirmed that the scaling form well explains the evolution of the cluster size distribution. Based on the distribution behavior, we find that a giant cluster of all oscillators is formed discontinuously at the threshold and also that further aggregation does not occur like in a one-dimensional bond percolation model. Finally, we discuss the origin of the discontinuous formation of the giant cluster from the perspective of global suppression in explosive percolation models. For this, we approximate the aggregation process as a cluster--cluster aggregation with a given collision kernel. We believe that the theoretical approach presented in this paper can be used to understand the transient dynamics of a broad range of synchronizations.
