Dynamics of clustering patterns in the Kuramoto model with unidirectional coupling

doi:10.1007/s11467-018-0783-1

Front. Phys.

2018, Vol. 13

Issue (5) : 130506 https://doi.org/10.1007/s11467-018-0783-1

RESEARCH ARTICLE

Dynamics of clustering patterns in the Kuramoto model with unidirectional coupling

Xia Huang^1,²(

), 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

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Abstract

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.

Keywords synchronization coupled phase oscillators phase transition

Corresponding Author(s): Xia Huang,Can Xu

Issue Date: 25 May 2018

Cite this article:

Xia Huang,Jin Dong,Wen-Jing Jia, et al. Dynamics of clustering patterns in the Kuramoto model with unidirectional coupling[J]. Front. Phys. , 2018, 13(5): 130506.

URL:

https://academic.hep.com.cn/fop/EN/10.1007/s11467-018-0783-1
https://academic.hep.com.cn/fop/EN/Y2018/V13/I5/130506

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