https://doi.org/10.1140/epjb/s10051-025-01015-z
Research - Statistical and Nonlinear Physics
Frequency-dependent synchronization in blinking networks: insights from Hindmarsh–Rose, Lorenz, and Rössler systems
1
School of Electronics and Communication Engineering, Shenzhen Polytechnic University, No.7089 Liuxian Avenue, 518055, Shenzhen, Guangdong, People’s Republic of China
2
School of Mathematics and Computer Science, Yan’an University, No.1 Gongxue North Road, 716000, Yan’an, Shaanxi, People’s Republic of China
3
Research and Development Department, Xi’an Congzheng New Energy Technology Co., Ltd., No. 2168, Zhenghe 4th Road, 712000, Xixian New Area, Shaanxi, People’s Republic of China
4
Institute of Electromechanical (Technician), Xianyang Vocational and Technical College, No.1 Unified Avenue, 712000, Xianyang, Shaanxi, People’s Republic of China
5
College of Engineering, South China Agricultural University, No.483 Wushan Road, 510642, Guangzhou, Shaanxi, People’s Republic of China
Received:
30
June
2025
Accepted:
29
July
2025
Published online:
7
August
2025
This study examines how the temporal structure of network couplings affects synchronization, a fundamental phenomenon in numerous real-world systems. Focusing on blinking networks, a class of time-varying networks where couplings periodically switch on and off, we compare two distinct blinking schemes across three canonical dynamical systems: the Hindmarsh–Rose, Lorenz, and Rössler systems. Using the Master Stability Function (MSF) framework, we reveal a striking contrast in synchronization behavior. When all couplings are activated simultaneously during the same portion of the blinking period, the system’s synchronization stability remains unaffected by the blinking frequency, closely resembling that of an averaged static network characterized by a linear MSF profile. In contrast, when couplings are activated sequentially within each blinking period, this linear MSF pattern emerges only at high blinking frequencies (fast blinking). At lower frequencies (slow blinking), the MSF exhibits diverse, system-specific patterns. Notably, the linear MSF pattern ensures the emergence of synchronization irrespective of the underlying structural properties. Thus, these findings offer new insights into how the temporal organization of couplings governs collective dynamics in time-varying networks, particularly in contexts where the emergence and stability of synchronization are critical.
Supplementary Information The online version contains supplementary material available at https://doi.org/10.1140/epjb/s10051-025-01015-z.
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Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
