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Multi-Cluster Flocking Behavior Analysis for a Delayed Cucker-Smale Model with Short-Range Communication Weight

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Abstract

This paper analyzes the multi-cluster flocking behavior of a Cucker-Smale model involving delays and a short-range communication weight. In each sub-flocking group, the velocity between agents is alignment and the position locates at a limited domain; but in different sub-flocking groups, the position between agents is unbounded. By constructing dissipative differential inequalities of sub-ensembles together with Lyapunov functional methods, the authors provide the sufficient condition for the multi-cluster flocking emerging. The sufficient condition includes the estimation of the range of coupling strength and the upper bound of time delay. As a result, the authors show that the coupling strength among agents and initial threshold value determine the multi-cluster flocking behavior of the delayed Cucker-Smale model.

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Authors and Affiliations

  1. Department of Mathematics, National University of Defense Technology, Changsha, 410073, China

    Zhengyang Qiao, Yicheng Liu & Xiao Wang

Authors
  1. Zhengyang Qiao
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  2. Yicheng Liu
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  3. Xiao Wang
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Corresponding authors

Correspondence to Zhengyang Qiao, Yicheng Liu or Xiao Wang.

Additional information

This research was supported by the National Natural Science Foundation of China under Grant Nos. 11671011 and 11428101.

This paper was recommended for publication by Editor YOU Keyou.

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Qiao, Z., Liu, Y. & Wang, X. Multi-Cluster Flocking Behavior Analysis for a Delayed Cucker-Smale Model with Short-Range Communication Weight. J Syst Sci Complex 35, 137–158 (2022). https://doi.org/10.1007/s11424-021-0026-3

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  • DOI: https://doi.org/10.1007/s11424-021-0026-3

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