Synchronization-desynchronization transitions in networks of circle maps with sinusoidal coupling

doi:10.1088/1674-1056/acc062

中国物理B ›› 2023, Vol. 32 ›› Issue (6): 60505-060505.doi: 10.1088/1674-1056/acc062

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

收稿日期:2023-02-09 修回日期:2023-02-22 接受日期:2023-03-02 出版日期:2023-05-17 发布日期:2023-05-17
通讯作者: Zhigang Zheng E-mail:zgzheng@bnu.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11875135).

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

Received:2023-02-09 Revised:2023-02-22 Accepted:2023-03-02 Online:2023-05-17 Published:2023-05-17
Contact: Zhigang Zheng E-mail:zgzheng@bnu.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11875135).

摘要/Abstract

摘要： 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.

关键词: synchronization, circle map, Kuramoto model, bifurcation

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.

Key words: synchronization, circle map, Kuramoto model, bifurcation

中图分类号: (Synchronization; coupled oscillators)

05.45.Xt

05.45.Ra (Coupled map lattices)

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[J]. 中国物理B, 2023, 32(6): 60505-060505.

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[J]. Chin. Phys. B, 2023, 32(6): 60505-060505.

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Synchronization-desynchronization transitions in networks of circle maps with sinusoidal coupling

Synchronization-desynchronization transitions in networks of circle maps with sinusoidal coupling

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