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<p>We study emergent behaviors of a discrete multi-cluster Cucker-Smale (MC-CS) model. The MC-CS model can be derived from the Cucker-Smale model under the <i>a priori</i> assumptions on the number of clusters and agents in each cluster. For the proposed model, we present a sufficient framework in terms of system parameters and initial data for the asymptotic emergence of a multi-clustering flocking configuration. Under the proposed sufficient framework, we show that the multi-cluster flocking configuration can emerge depending on the decay mode of the communication weight function. We also provide several numerical simulations and compare them with theoretical results.</p>

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On the asymptotic robustness of multi-cluster flocking configurations in the discrete Cucker-Smale model

  • 期刊论文

  • 发表日期：

    2026年7月22日

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  • Seung-Yeal Ha,
  • Chunyin Jin,
  • Myeonghyeon Kim,
  • Yinglong Zhang

摘要

We study emergent behaviors of a discrete multi-cluster Cucker-Smale (MC-CS) model. The MC-CS model can be derived from the Cucker-Smale model under the a priori assumptions on the number of clusters and agents in each cluster. For the proposed model, we present a sufficient framework in terms of system parameters and initial data for the asymptotic emergence of a multi-clustering flocking configuration. Under the proposed sufficient framework, we show that the multi-cluster flocking configuration can emerge depending on the decay mode of the communication weight function. We also provide several numerical simulations and compare them with theoretical results.