Dynamics of clustering patterns in the Kuramoto model with unidirectional coupling
Xia Huang1,2(), Jin Dong1, Wen-Jing Jia3, Zhi-Gang Zheng3, Can Xu3()
1. School of Mathematics and Physics, North China Electric Power University, Beijing 102206, China 2. Cardiovascular Research Laboratories, Departments of Medicine and Biomathematics, David Geffen School of Medicine, University of California, Los Angeles, Los Angeles, CA 90095, USA 3. Institute of Systems Science and College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
We study the synchronization transition in the Kuramoto model by considering a unidirectional coupling with a chain structure. The microscopic clustering features are characterized in the system. We identify several clustering patterns for the long-time evolution of the effective frequencies and reveal the phase transition between them. Theoretically, the recursive approach is developed in order to obtain analytical insights; the essential bifurcation schemes of the clustering patterns are clarified and the phase diagram is illustrated in order to depict the various phase transitions of the system. Furthermore, these recursive theories can be extended to a larger system. Our theoretical analysis is in agreement with the numerical simulations and can aid in understanding the clustering patterns in the Kuramoto model with a general structure.
. [J]. Frontiers of Physics, 2018, 13(5): 130506.
Xia Huang, Jin Dong, Wen-Jing Jia, Zhi-Gang Zheng, Can Xu. Dynamics of clustering patterns in the Kuramoto model with unidirectional coupling. Front. Phys. , 2018, 13(5): 130506.
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