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Time and energy costs for cluster synchronization in Kuramoto-oscillator networks under pinning strategies

Author

Listed:
  • Zhu, Jian
  • Li, Wang
  • Yin, Xiangxin
  • Chang, Jiaqi
  • Zhao, Donghua
  • Sun, Yongzheng

Abstract

Time and energy costs are critical considerations in the practical implementation of synchronization strategies for Kuramoto-oscillator networks. However, the fundamental problem of how to minimize the control cost of achieving multi-objective cluster synchronization within a predefined time remains unresolved. To address this issue, novel cluster synchronization strategies based on finite-time and predefined-time control techniques are proposed. The proposed method avoids chattering phenomena and ensures synchronization by controlling only a single oscillator within each cluster. Sufficient conditions for achieving finite-time and predefined-time synchronization are established, and an upper bound on energy cost for predefined-time cluster synchronization is derived. Specifically, under a predefined convergence time, increasing the number of pinned oscillators facilitates synchronization at the cost of higher energy consumption.

Suggested Citation

  • Zhu, Jian & Li, Wang & Yin, Xiangxin & Chang, Jiaqi & Zhao, Donghua & Sun, Yongzheng, 2026. "Time and energy costs for cluster synchronization in Kuramoto-oscillator networks under pinning strategies," Chaos, Solitons & Fractals, Elsevier, vol. 204(C).
    • Handle: RePEc:eee:chsofr:v:204:y:2026:i:c:s0960077925017667
    DOI: 10.1016/j.chaos.2025.117752
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    1. Kar, Rumi & Nair, Gokul B. & Chandrasekar, V.K. & Senthilkumar, D.V., 2025. "Chimera states in a globally coupled bipartite network with higher-order interaction," Chaos, Solitons & Fractals, Elsevier, vol. 192(C).
    2. Kim, Cook Hyun & Park, Jinha & Kim, Young Jin & Park, Sangjoon & Boccaletti, S. & Kahng, B., 2025. "Cluster-mediated synchronization dynamics in globally coupled oscillators with inertia," Chaos, Solitons & Fractals, Elsevier, vol. 196(C).
    3. Zhang, Ruoqi & Lin, Lifeng & Wang, Huiqi, 2025. "Synchronization resilience of coupled fluctuating-damping oscillators in small-world weighted complex networks," Chaos, Solitons & Fractals, Elsevier, vol. 190(C).
    4. Ma, Weiyuan & Ma, Chenjun & Wang, Xiaoqin & Sun, Weigang, 2025. "Delayed control-based controllability of discrete fractional higher-order neural networks," Chaos, Solitons & Fractals, Elsevier, vol. 200(P1).
    5. Li, Kezan & Lin, Yingmei & Wang, Junyi, 2024. "Synchronization of multi-directed hypergraphs via adaptive pinning control," Chaos, Solitons & Fractals, Elsevier, vol. 184(C).
    6. Xu, Xu & Yan, Tingruo & Li, Eric, 2025. "Chattering-free control of chaotic synchronization within a fixed timeframe," Chaos, Solitons & Fractals, Elsevier, vol. 194(C).
    7. Wang, Yi & Zhao, Yi, 2024. "Synchronization of directed higher-order networks via pinning control," Chaos, Solitons & Fractals, Elsevier, vol. 185(C).
    8. Xu, Can & Zhai, Yun & Wu, Yonggang & Zheng, Zhigang & Guan, Shuguang, 2023. "Enhanced explosive synchronization in heterogeneous oscillator populations with higher-order interactions," Chaos, Solitons & Fractals, Elsevier, vol. 170(C).
    9. Zhu, Yuying & Xing, Bohua & Xia, Chengyi, 2025. "Q-learning update with second-order reputation promotes the evolution of trust within structured populations," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    10. Li, Tianyu & Xie, Ying & Ye, Zhiqiu & Zeng, Jiapei & Liu, Yingqi & Liu, Lu & Jia, Ya, 2025. "Analysis of synchronization transitions in higher-order Kuramoto oscillator system with different orders of phase lags," Chaos, Solitons & Fractals, Elsevier, vol. 199(P1).
    11. Shi, Jinyao & Zhou, Peipei & Cai, Shuiming, 2024. "On fixed-time interlayer synchronization of two-layer multiweighted complex dynamic networks: An economic and practical non-chattering adaptive control approach," Chaos, Solitons & Fractals, Elsevier, vol. 182(C).
    12. Surendar, R. & Muthtamilselvan, M. & Ahn, Kyubok, 2024. "Stochastic disturbance with finite-time chaos stabilization and synchronization for a fractional-order nonautonomous hybrid nonlinear complex system via a sliding mode control," Chaos, Solitons & Fractals, Elsevier, vol. 181(C).
    13. Bo-Wei Qin & Lei Zhao & Wei Lin, 2021. "A frequency-amplitude coordinator and its optimal energy consumption for biological oscillators," Nature Communications, Nature, vol. 12(1), pages 1-13, December.
    14. Guo, Junfeng & Wang, Fei & Xue, Qianwen & Wang, Mengqing, 2023. "Cluster synchronization control for coupled genetic oscillator networks under denial-of-service attacks: Pinning partial impulsive strategy," Chaos, Solitons & Fractals, Elsevier, vol. 177(C).
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