Non-flocking and flocking for the Cucker-Smale model with distributed time delays

Ziwei Zhang, Xiuxia Yin*, Zhiwei Gao

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)
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Abstract

In this paper, we study a flocking behavior that may or not appear for Cucker - Smale model with distributed time delays. For the short range communicated Cucker - Smale model, the flocking condition has strong restrictions on initial data. For this case, we mainly consider the non - flocking behavior. By establishing and appropriately estimating an inequality of the position variance such that the second order space moment is unbounded, we drive a sufficient condition for the non - existence of the asymptotic flocking when the time delays satisfy a suitable smallness assumption. Furthermore, we also provide a sufficient condition of asymptotic flocking. Finally, we present numerical simulations to validate the theoretical results.

Original languageEnglish
Pages (from-to)8788-8805
JournalJournal of the Franklin Institute
Volume360
Issue number12
Early online date2 Apr 2022
DOIs
Publication statusPublished - 1 Aug 2023

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