Li Xue, Zhang Jiameng, Zou Yong, Guan Shuguang
Department of Physics, East China Normal University, Shanghai 200241, China.
Chaos. 2019 Apr;29(4):043102. doi: 10.1063/1.5085407.
In this paper, clustering in the Kuramoto model with second-order coupling is investigated under the bimodal Lorentzian frequency distribution. By linear stability analysis and the Ott-Antonsen ansatz treatment, the critical coupling strength for the synchronization transition is obtained. The theoretical results are further verified by numerical simulations. It has been revealed that various synchronization paths, including the first- and second-order transitions as well as the multiple bifurcations, exist in this system with different parameters of frequency distribution. In certain parameter regimes, the Bellerophon states are observed and their dynamical features are fully characterized.
本文研究了在双峰洛伦兹频率分布下具有二阶耦合的Kuramoto模型中的聚类现象。通过线性稳定性分析和Ott-Antonsen假设处理，得到了同步转变的临界耦合强度。理论结果通过数值模拟进一步验证。结果表明，在该具有不同频率分布参数的系统中，存在各种同步路径，包括一阶和二阶转变以及多重分岔。在某些参数区域中，观察到了贝洛丰态并对其动力学特征进行了全面表征。
