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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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