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

Zhang, Ziwei, Yin, Xiuxia and Gao, Zhiwei (2022) Non-flocking and flocking for the Cucker-Smale model with distributed time delays. Journal of the Franklin Institute. ISSN 0016-0032 (In Press)

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Official URL: https://doi.org/10.1016/j.jfranklin.2022.03.028

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.

Item Type: Article
Additional Information: Funding Information: This work is supported by NSFC (No. 61963028 and No. 61603175) and the Jiangxi Province academic and technical leader Training ProgramYoung Talents Project (20212BCJ23040).
Uncontrolled Keywords: Cucker−Smale model, distributed time delays, non−flocking, flocking.
Subjects: G400 Computer Science
G900 Others in Mathematical and Computing Sciences
Department: Faculties > Engineering and Environment > Mathematics, Physics and Electrical Engineering
Depositing User: Rachel Branson
Date Deposited: 17 May 2022 11:21
Last Modified: 17 May 2022 11:30
URI: http://nrl.northumbria.ac.uk/id/eprint/49143

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