Flocking dynamics and pattern motion for the Cucker-Smale system with distributed delays

Jingyi He; Changchun Bao; Le Li; Xianhui Zhang; Chuangxia Huang; Jingyi He; Changchun Bao; Le Li; Xianhui Zhang; Chuangxia Huang

doi:10.3934/mbe.2023068

Mathematical Biosciences and Engineering

2023, Volume 20, Issue 1: 1505-1518. doi: 10.3934/mbe.2023068

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Research article Special Issues

Flocking dynamics and pattern motion for the Cucker-Smale system with distributed delays

1.
School of Mathematics and Statistics, Changsha University of Science and Technology, Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha 410114, China
2.
School of Meteorology and Oceanography, National University of Defense Technology, Changsha 410073, China

† The authors contributed equally to this work.
Academic Editor: Xiaodi Li

Received: 02 September 2022 Revised: 13 October 2022 Accepted: 21 October 2022 Published: 02 November 2022

In this paper, a new class of Cucker-Smale systems with distributed delays are developed from the measurement perspective. By combining dissipative differential inequalities with a continuity argument, some new sufficient criteria for the flocking dynamics of the proposed model with general communication rate, especially the non-normalized rate, are established. In order to achieve the prescribed pattern motion, the driving force term is incorporated into the delayed collective system. Lastly, some examples and simulations are provided to illustrate the validity of the theoretical results.
- Cucker-Smale model,
- flocking behavior,
- distributed delay,
- pattern motion
Citation: Jingyi He, Changchun Bao, Le Li, Xianhui Zhang, Chuangxia Huang. Flocking dynamics and pattern motion for the Cucker-Smale system with distributed delays[J]. Mathematical Biosciences and Engineering, 2023, 20(1): 1505-1518. doi: 10.3934/mbe.2023068

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Abstract

In this paper, a new class of Cucker-Smale systems with distributed delays are developed from the measurement perspective. By combining dissipative differential inequalities with a continuity argument, some new sufficient criteria for the flocking dynamics of the proposed model with general communication rate, especially the non-normalized rate, are established. In order to achieve the prescribed pattern motion, the driving force term is incorporated into the delayed collective system. Lastly, some examples and simulations are provided to illustrate the validity of the theoretical results.

References

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