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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

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

  • 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.

    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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  • 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.




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