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The collision-avoiding flocking of a Cucker–Smale model with pinning control and external perturbation

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  • Ren, Jianlong
  • Liu, Qiming
  • Li, Ping

Abstract

The Cucker–Smale model is an essential and effective tool for analyzing flocking behavior. A modified Cucker–Smale model with pinning control and external perturbation is proposed in this paper. Primarily, by imposing appropriate restrictions on external perturbation, the system can achieve asymptotic flocking; simultaneously, pinning control improves the speed of flocking. Furthermore, collision-avoiding between any two agents in the flocking process can be derived. The results show that the convergence time depends on control parameters and the convergence speed of the perturbation. Lastly, some numerical simulations are given to illustrate the effectiveness of the theoretical results.

Suggested Citation

  • Ren, Jianlong & Liu, Qiming & Li, Ping, 2025. "The collision-avoiding flocking of a Cucker–Smale model with pinning control and external perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 665(C).
    • Handle: RePEc:eee:phsmap:v:665:y:2025:i:c:s0378437125001189
    DOI: 10.1016/j.physa.2025.130466
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    References listed on IDEAS

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    1. Li, Le & Yan, Lifen & Huang, Chuangxia & Cao, Jinde & Ding, Xiaodan, 2024. "Linear formation of Cucker–Smale model with distributed time delays," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 222(C), pages 296-310.
    2. Adsadang Himakalasa & Suttida Wongkaew & Miaomiao Wang, 2021. "Optimal Control through Leadership of the Cucker and Smale Flocking Model with Time Delays," Complexity, Hindawi, vol. 2021, pages 1-14, August.
    3. Zhao, Rundong & Liu, Qiming & Zhang, Huazong, 2022. "Flocking and collision avoidance problem of a singular Cucker–Smale model with external perturbations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    4. Wang, Mengchen & Lu, Xiaowen & Yang, Qi & Ma, Zhongjun & Cheng, Jun & Li, Kezan, 2022. "Pinning control of successive lag synchronization on a dynamical network with noise perturbation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 593(C).
    5. Hongliang Liu & Xiao Wang & Xiang Li & Yicheng Liu, 2020. "Finite-time flocking and collision avoidance for second-order multi-agent systems," International Journal of Systems Science, Taylor & Francis Journals, vol. 51(1), pages 102-115, January.
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