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

Ziwei Zhang; Xiuxia Yin; Zhiwei Gao

doi:10.1016/j.jfranklin.2022.03.028

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

Ziwei Zhang, Xiuxia Yin^*, Zhiwei Gao

^*Corresponding author for this work

Mathematics, Physics and Electrical Engineering

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

13 Downloads (Pure)

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 language	English
Pages (from-to)	8788-8805
Journal	Journal of the Franklin Institute
Volume	360
Issue number	12
Early online date	2 Apr 2022
DOIs	https://doi.org/10.1016/j.jfranklin.2022.03.028
Publication status	Published - 1 Aug 2023

Keywords

Cucker−Smale model
distributed time delays
non−flocking
flocking

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10.1016/j.jfranklin.2022.03.028

AAMAccepted author manuscript, 363 KBLicence: CC BY-NC-ND

Cite this

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title = "Non-flocking and flocking for the Cucker-Smale model with distributed time delays",

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.",

keywords = "Cucker−Smale model, distributed time delays, non−flocking, flocking",

author = "Ziwei Zhang and Xiuxia Yin and Zhiwei Gao",

note = "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). ",

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doi = "10.1016/j.jfranklin.2022.03.028",

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T1 - Non-flocking and flocking for the Cucker-Smale model with distributed time delays

AU - Zhang, Ziwei

AU - Yin, Xiuxia

AU - Gao, Zhiwei

N1 - 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).

PY - 2023/8/1

Y1 - 2023/8/1

N2 - 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.

AB - 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.

KW - Cucker−Smale model

KW - distributed time delays

KW - non−flocking

KW - flocking

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U2 - 10.1016/j.jfranklin.2022.03.028

DO - 10.1016/j.jfranklin.2022.03.028

M3 - Article

AN - SCOPUS:85128652242

SN - 0016-0032

VL - 360

SP - 8788

EP - 8805

JO - Journal of the Franklin Institute

JF - Journal of the Franklin Institute

IS - 12

ER -

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

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Keywords

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