Wang Chengwei, Rubido Nicolás, Grebogi Celso, Baptista Murilo S
Institute for Complex Systems and Mathematical Biology, University of Aberdeen, King's College, AB24 3UE Aberdeen, United Kingdom.
Instituto de Física, Facultad de Ciencias, Universidad de la República, Iguá 4225, 11400 Montevideo, Uruguay.
Phys Rev E Stat Nonlin Soft Matter Phys. 2015 Dec;92(6):062808. doi: 10.1103/PhysRevE.92.062808. Epub 2015 Dec 8.
Scientists have been considering the Kuramoto model to understand the mechanism behind the appearance of collective behavior, such as frequency synchronization (FS) as a paradigm, in real-world networks with a finite number of oscillators. A major current challenge is to obtain an analytical solution for the phase angles. Here, we provide an approximate analytical solution for this problem by deriving a master solution for the finite-size Kuramoto model, with arbitrary finite-variance distribution of the natural frequencies of the oscillators. The master solution embodies all particular solutions of the finite-size Kuramoto model for any frequency distribution and coupling strength larger than the critical one. Furthermore, we present a criterion to determine the stability of the FS solution. This allows one to analytically infer the relationship between the physical parameters and the stable behavior of networks.
科学家们一直在研究Kuramoto模型，以理解在具有有限数量振子的现实世界网络中集体行为出现背后的机制，例如以频率同步（FS）作为范例。当前一个主要挑战是获得相位角的解析解。在此，我们通过推导有限尺寸Kuramoto模型的主解，为该问题提供了一个近似解析解，振子的自然频率具有任意有限方差分布。主解体现了有限尺寸Kuramoto模型对于任何频率分布以及大于临界耦合强度的所有特定解。此外，我们提出了一个确定FS解稳定性的准则。这使得人们能够从解析上推断物理参数与网络稳定行为之间的关系。
