Dynamics of clustering patterns in the Kuramoto model with unidirectional coupling

• Published in: Frontiers of physics Vol. 13; no. 5; p. 130506
• Main Authors: Huang, Xia, Dong, Jin, Jia, Wen-Jing, Zheng, Zhi-Gang, Xu, Can
• Format: Journal Article
• Language: English
• Published: Beijing Higher Education Press 01.10.2018; Springer Nature B.V
• Subjects: Astronomy; Astrophysics and Cosmology; Atomic; Clustering; Condensed Matter Physics; coupled phase oscillators; Coupling; Mathematical models; Molecular; Optical and Plasma Physics; Oscillators; Particle and Nuclear Physics; Phase diagrams; phase transition; Phase transitions; Physics; Physics and Astronomy; Recursive methods; Research Article; Synchronism; synchronization; Theoretical analysis; synchronization; coupled phase oscillators; phase transition
• ISSN: 2095-0462; 2095-0470
• DOI: 10.1007/s11467-018-0783-1

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.