Synchronization-desynchronization transitions in networks of circle maps with sinusoidal coupling
Yun Zhai(翟云)1,2,3, Jinghua Xiao(肖井华)1, and Zhigang Zheng(郑志刚)2,3,†
1 School of Science, Beijing University of Posts and Telecommunications, Beijing 100876, China; 2 Institute of Systems Science, Huaqiao University, Xiamen 361021, China; 3 College of Information Science and Engineering, Huaqiao University, Xiamen 361021, China
Abstract Coupled phase oscillators are adopted as powerful platforms in studying synchrony behaviors emerged in various systems with rhythmic dynamics. Much attention has been focused on coupled time-continuous oscillators described by differential equations. In this paper, we study the synchronization dynamics of networks of coupled circle maps as the discrete version of the Kuramoto model. Despite of its simplicity in mathematical form, it is found that discreteness may induce many interesting synchronization behaviors. Multiple synchronization and desynchronization transitions of both phases and frequencies are found with varying the coupling among circle-map oscillators. The mechanisms of these transitions are interpreted in terms of the mean-field approach, where collective bifurcation cascades are revealed for coupled circle-map oscillators.
Yun Zhai(翟云), Jinghua Xiao(肖井华), and Zhigang Zheng(郑志刚) Synchronization-desynchronization transitions in networks of circle maps with sinusoidal coupling 2023 Chin. Phys. B 32 060505
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