Directed acyclic decomposition of Kuramoto equations.
Directed acyclic decomposition of Kuramoto equations.
复制标题
Kuramoto 方程的定向非循环分解。
作者：
Tianran Chen
仓本模型是描述耦合振子网络中同步行为的研究最广泛的模型之一，它有着广泛的应用。由于复杂的非线性相互作用，在一般非均匀、异构和稀疏网络中找到所有可能的频率同步配置很重要，但也具有挑战性。从同伦变形的角度出发，提出了一个将Kuramoto网络分解为更小的有向无环子网络的一般框架，为用分治法研究大型Kuramoto网络的频率同步结构奠定了基础.
The Kuramoto model is one of the most widely studied models for describing synchronization behaviors in a network of coupled oscillators, and it has found a wide range of applications. Finding all possible frequency synchronization configurations in a general nonuniform, heterogeneous, and sparse network is important yet challenging due to complicated nonlinear interactions. From the view point of homotopy deformation, we develop a general framework for decomposing a Kuramoto network into smaller directed acyclic subnetworks, which lays the foundation for a divide-and-conquer approach to studying the configurations of frequency synchronization of large Kuramoto networks.