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

Hyunjin Ahn; Hyunjin Ahn

doi:10.3934/nhm.2023002

Networks and Heterogeneous Media

2023, Volume 18, Issue 1: 29-47. doi: 10.3934/nhm.2023002

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Research article

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

Hyunjin Ahn ^,

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

Received: 19 September 2022 Revised: 05 October 2022 Accepted: 11 October 2022 Published: 19 October 2022

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.
- Asymptotic flocking,
- dissipative structure,
- relativistic Cucker–Smale,
- time delay
Citation: Hyunjin Ahn. Asymptotic flocking of the relativistic Cucker–Smale model with time delay[J]. Networks and Heterogeneous Media, 2023, 18(1): 29-47. doi: 10.3934/nhm.2023002

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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.

References

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