在从众和反向振荡器同步过程中的朗道阻尼效应。

Landau damping effects in the synchronization of conformist and contrarian oscillators.

作者信息

Qiu Tian, Zhang Yue, Liu Jie, Bi Hongjie, Boccaletti S, Liu Zonghua, Guan Shuguang

机构信息

Department of Physics, East China Normal University, Shanghai, 200241, China.

CNR-Institute of Complex Systems, Via Madonna del Piano, 10, 50019 Sesto Fiorentino, Florence, Italy.

出版信息

Sci Rep. 2015 Dec 14;5:18235. doi: 10.1038/srep18235.

DOI:10.1038/srep18235

PMID:26657060

原文链接:https://pmc.ncbi.nlm.nih.gov/articles/PMC4677401/

Abstract

Two decades ago, a phenomenon resembling Landau damping was described in the synchronization of globally coupled oscillators: the evidence of a regime where the order parameter decays when linear theory predicts neutral stability for the incoherent state. We here show that such an effect is far more generic, as soon as phase oscillators couple to their mean field according to their natural frequencies, being then grouped into two distinct populations of conformists and contrarians. We report the analytical solution of this latter situation, which allows determining the critical coupling strength and the stability of the incoherent state, together with extensive numerical simulations that fully support all theoretical predictions. The relevance of our results is discussed in relationship to collective phenomena occurring in social and economical systems.

摘要

二十年前，在全局耦合振子的同步中描述了一种类似于朗道阻尼的现象：存在一种状态的证据，即当线性理论预测非相干态为中性稳定时，序参量会衰减。我们在此表明，只要相位振子根据其固有频率与其平均场耦合，然后分为顺应者和反对者这两个不同群体，这种效应就更为普遍。我们报告了后一种情况的解析解，它可以确定临界耦合强度和非相干态的稳定性，同时还有广泛的数值模拟充分支持所有理论预测。我们结合社会和经济系统中发生的集体现象讨论了我们结果的相关性。