Um Jaegon, Hong Hyunsuk, Park Hyunggyu
School of Physics, Korea Institute for Advanced Study, Seoul 130-722, Korea.
Department of Physics and Research Institute of Physics and Chemistry, Chonbuk National University, Jeonju 561-756, Korea.
Phys Rev E Stat Nonlin Soft Matter Phys. 2014 Jan;89(1):012810. doi: 10.1103/PhysRevE.89.012810. Epub 2014 Jan 22.
We consider a system of phase oscillators with random intrinsic frequencies coupled through sparse random networks and investigate how the connectivity disorder affects the nature of collective synchronization transitions. Various distribution types of intrinsic frequencies are considered: uniform, unimodal, and bimodal distribution. We employ a heterogeneous mean-field approximation based on the annealed networks and also perform numerical simulations on the quenched Erdös-Rényi networks. We find that the connectivity disorder drastically changes the nature of the synchronization transitions. In particular, the quenched randomness completely wipes away the diversity of the transition nature, and only a continuous transition appears with the same mean-field exponent for all types of frequency distributions. The physical origin of this unexpected result is discussed.
我们考虑一个具有随机固有频率的相位振子系统，这些振子通过稀疏随机网络相互耦合，并研究连接无序如何影响集体同步转变的性质。我们考虑了固有频率的各种分布类型：均匀分布、单峰分布和双峰分布。我们采用基于退火网络的非均匀平均场近似，并在淬火的厄多斯-雷尼网络上进行数值模拟。我们发现连接无序极大地改变了同步转变的性质。特别是，淬火随机性完全消除了转变性质的多样性，对于所有类型的频率分布，只出现具有相同平均场指数的连续转变。我们讨论了这一意外结果的物理根源。
