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Flocking of a Cucker–Smale Type Model with Compactly Supported Interaction Functions

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Abstract

How to analyze flocking behaviors of a multi-agent system with local interaction functions is a challenging problem in theory. Motsch and Tadmor in 2011 also stressed the significance to assume that the interaction function is rapidly decaying or cut-off at a finite distance (cf. Motsch and Tadmor in J. Stat. Phys. 2011). In this paper, we study the flocking behavior of a Cucker–Smale type model with compactly supported interaction functions. Using properties of a connected stochastic matrix, together with an elaborate analysis on perturbations of a linearized system, we obtain a sufficient condition imposed only on model parameters and initial data to guarantee flocking. Moreover, it is shown that the system achieves flocking at an exponential rate.

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Acknowledgements

We thank the referees for their time and comments.

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Authors and Affiliations

  1. College of Science, China Agricultural University, Beijing, 100083, P. R. China

    Chun Yin Jin & Shuang Zhi Li

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  1. Chun Yin Jin
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  2. Shuang Zhi Li
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Correspondence to Chun Yin Jin.

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Conflict of Interest The authors declare no conflict of interest.

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The first author is supported by NSFC (Grant No. 12001530)

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Jin, C.Y., Li, S.Z. Flocking of a Cucker–Smale Type Model with Compactly Supported Interaction Functions. Acta. Math. Sin.-English Ser. 40, 2285–2296 (2024). https://doi.org/10.1007/s10114-024-2127-0

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  • DOI: https://doi.org/10.1007/s10114-024-2127-0

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