Ling Xiang, Ju Wen-Bin, Guo Ning, Zhu Kong-Jin, Wu Chao-Yun, Hao Qing-Yi
School of Automotive and Transportation Engineering, Hefei University of Technology, 230009 Hefei, People's Republic of China.
School of Mathematics and Physics, Anqing Normal University, Anqing 246133, People's Republic of China.
Chaos. 2022 Jan;32(1):013118. doi: 10.1063/5.0058747.
Synchronization is a ubiquitous phenomenon in engineering and natural ecosystems. While the dynamics of synchronization modeled by the Kuramoto model are commonly studied in two dimensions and the state of dynamic units is characterized by a scalar angle variable, we studied the Kuramoto model generalized to D dimensions in the framework of a complex network and utilized the local synchronous order parameter between the agent and its neighbors as the controllable variable to adjust the coupling strength. Here, we reported that average connectivity of networks affects the time-dependent, rhythmic, cyclic state. Importantly, we found that the level of heterogeneity of networks governs the rhythmic state in the transition process. The analytical treatment for observed scenarios in a D-dimensional Kuramoto model at D=3 was provided. These results offered a platform for a better understanding of time-dependent swarming and flocking dynamics in nature.
同步是工程和自然生态系统中普遍存在的现象。虽然由Kuramoto模型建模的同步动力学通常在二维中进行研究，并且动态单元的状态由标量角度变量表征，但我们在复杂网络框架下研究了推广到D维的Kuramoto模型，并利用智能体与其邻居之间的局部同步序参量作为可控变量来调整耦合强度。在此，我们报告了网络的平均连通性会影响随时间变化的、有节奏的循环状态。重要的是，我们发现网络的异质性水平在过渡过程中控制着节奏状态。提供了对三维D维Kuramoto模型中观察到的场景的解析处理。这些结果为更好地理解自然界中随时间变化的群体和聚集动力学提供了一个平台。
