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Research Article | Open Access

Asymptotic flocking of the relativistic Cucker–Smale model with time delay

Department of Mathematical Sciences and Research Institute of Mathematics, Seoul National University, Seoul, Republic of Korea
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Abstract

This paper presents various sufficient conditions for asymptotic flocking in the relativistic Cucker–Smale (RCS) model with time delay. This model considers a self-processing time delay. We reduce the time-delayed RCS model to its dissipative structure for relativistic velocities. Then, using this dissipative structure, we demonstrate several sufficient frameworks in terms of the initial data and system parameters for asymptotic flocking of the proposed model.

Keywords

Asymptotic flockingdissipative structurerelativistic Cucker–Smaletime delay

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Networks and Heterogeneous Media
Volume 18 Issue 1,
March 2023
Pages 29-47
DOI: 10.3934/nhm.2023002

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Ahn H. Asymptotic flocking of the relativistic Cucker–Smale model with time delay. Networks and Heterogeneous Media, 2023, 18(1): 29-47. https://doi.org/10.3934/nhm.2023002

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Received: 19 September 2022
Revised: 05 October 2022
Accepted: 11 October 2022
Published: 15 March 2023
©2023 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)