Non-emergence of mono-cluster flocking and multi-cluster flocking of the thermodynamic Cucker–Smale model with a unit-speed constraint

Hyunjin Ahn; Hyunjin Ahn

doi:10.3934/nhm.2023066

Networks and Heterogeneous Media

2023, Volume 18, Issue 4: 1493-1527. doi: 10.3934/nhm.2023066

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Research article

Non-emergence of mono-cluster flocking and multi-cluster flocking of the thermodynamic Cucker–Smale model with a unit-speed constraint

Hyunjin Ahn ^,

Department of Mathematics, Myongji University, Gyeonggi-do 17058, Republic of Korea

Received: 19 April 2023 Revised: 12 June 2023 Accepted: 16 June 2023 Published: 12 July 2023

This paper demonstrates several sufficient frameworks for the mono-cluster flocking, the non-emergence of mono-cluster flocking and the multi-cluster flocking of the thermodynamic Cucker–Smale model with a unit-speed constraint (say TCSUS). First, in a different way than ^[2], we present the admissible data for the mono-cluster flocking of TCSUS to occur. Second, we prove that when the coupling strength is less than some positive value, mono-cluster flocking does not occur in the TCSUS system with an integrable communication weight. Third, motivated from the study on coupling strengths where the mono-cluster flocking does not occur, we investigate appropriate sufficient frameworks to derive the multi-cluster flocking of the TCSUS system.
- Cucker–Smale,
- mono-cluster flocking,
- multi-agent system,
- multi-cluster flocking,
- thermodynamic,
- unit-speed
Citation: Hyunjin Ahn. Non-emergence of mono-cluster flocking and multi-cluster flocking of the thermodynamic Cucker–Smale model with a unit-speed constraint[J]. Networks and Heterogeneous Media, 2023, 18(4): 1493-1527. doi: 10.3934/nhm.2023066

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Abstract

This paper demonstrates several sufficient frameworks for the mono-cluster flocking, the non-emergence of mono-cluster flocking and the multi-cluster flocking of the thermodynamic Cucker–Smale model with a unit-speed constraint (say TCSUS). First, in a different way than ^[2], we present the admissible data for the mono-cluster flocking of TCSUS to occur. Second, we prove that when the coupling strength is less than some positive value, mono-cluster flocking does not occur in the TCSUS system with an integrable communication weight. Third, motivated from the study on coupling strengths where the mono-cluster flocking does not occur, we investigate appropriate sufficient frameworks to derive the multi-cluster flocking of the TCSUS system.

References

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