基于重整化群的同步分析
首发时间:2020-09-03
摘要:本文基于重整化群方法对Kuramoto模型进行解析分析。通过微扰展开消除共振项,提出重整化频率和频率修正项的概念。将振子消除暂态这个连续时间的过程看作一个从初态到终态的非连续过程。在低维情况下,重整化频率与数值求解的平均频率符合较好。在高维情况下,可以帮助更好的理解平均频率,临界耦合强度之间的关系。并证明了自然频率服从线性分布的大振子群按照一定拓扑结构排列,同步比例与临界耦合强度线性相关的合理性。
关键词: 理论物理 重整化群 Kuramoto模型 重整化频率 频率修正项
For information in English, please click here
Renormalization group analysis of synchronization
Abstract:Based on the renormalization group method, we analyze the Kuramoto oscillator model. The concept of renormalized frequency and frequency correction term is proposed by using perturbation expansion to eliminate resonance terms. The continuous frequency correction of the oscillator during the transient is treated as a discontinuous jump from the generic to the renormalized state.In the low dimensional case, the renormalization frequency is in good agreement with the average frequency of the numerical solution. In the high-dimensional case, it can help to better understand the relationship between the average frequency and the critical coupling strength. It is proved that when the large oscillator groups with linear natural frequencies are arranged in certain way, the synchronization ratio is linearly related to the critical coupling strength.
Keywords: Theoretical physics renormalization group Kuramoto model renormalization frequency frequency correction term
引用
No.****
动态公开评议
共计0人参与
勘误表
基于重整化群的同步分析
评论
全部评论0/1000