The delayed Cucker-Smale model with short range communication weights

Zili Chen; Xiuxia Yin

doi:10.3934/krm.2021030

Article Contents

2021, Volume 14, Issue 6: 929-948. Doi: 10.3934/krm.2021030

This issue Previous Article Next Article Relativistic BGK model for massless particles in the FLRW spacetime

The delayed Cucker-Smale model with short range communication weights

Zili Chen and
Xiuxia Yin^,

Department of Mathematics, School of Science, Nanchang University, Nanchang, Jiangxi 330031, China

^* Corresponding author
^* Corresponding author

Received: February 28, 2021

Revised: June 30, 2021

Early access: September 2021

Published: December 2021

The first author is supported by NSFC grant 11961046. The second author is supported by NSFC grant 61963028) and Natural Science Foundation of Jiangxi Province grant 20192BAB207023

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Abstract

Various flocking results have been established for the delayed Cucker-Smale model, especially in the long range communication case. However, the short range communication case is more realistic due to the limited communication ability. In this case, the non-flocking behavior can be frequently observed in numerical simulations. Furthermore, it has potential applications in many practical situations, such as the opinion disagreement in society, fish flock breaking and so on. Therefore, we firstly consider the non-flocking behavior of the delayed Cucker$ - $Smale model. Based on a key inequality of position variance, a simple sufficient condition of the initial data to the non-flocking behavior is established. Then, for general communication weights we obtain a flocking result, which also depends upon the initial data in the short range communication case. Finally, with no restriction on the initial data we further establish other large time behavior of classical solutions.

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Mathematics Subject Classification: Primary: 35F25, 35J05; Secondary: 35Q83, 82C40.

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