EMERGENT BEHAVIOR OF CLOSEST NEIGHBORS MODEL WITH NONLINEAR INHERENT DYNAMICS

doi:10.1007/s10473-025-0421-2

数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (4): 1640-1658.doi: 10.1007/s10473-025-0421-2

EMERGENT BEHAVIOR OF CLOSEST NEIGHBORS MODEL WITH NONLINEAR INHERENT DYNAMICS

Yuan LIANG¹, Chen WU^1,2, Jiugang DONG^1,*

1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;
2. School of Mathematical and Big Data, Anhui University of Science and Technology, Huainan 232001, China

收稿日期:2024-06-19 出版日期:2025-10-10 发布日期:2025-10-10

EMERGENT BEHAVIOR OF CLOSEST NEIGHBORS MODEL WITH NONLINEAR INHERENT DYNAMICS

Yuan LIANG¹, Chen WU^1,2, Jiugang DONG^1,*

1. School of Mathematical Sciences, Dalian University of Technology, Dalian 116024, China;
2. School of Mathematical and Big Data, Anhui University of Science and Technology, Huainan 232001, China

Received:2024-06-19 Online:2025-10-10 Published:2025-10-10
Contact: ^*Jiugang DONG, E-mail: jgdong@dlut.edu.cn
About author:Yuan LIANG, E-mail: liangyuan@mail.dlut.edu.cn; Chen WU, E-mail: wuchen@aust.edu.cn
Supported by:
National Key R&D Program of China (2023Y-FA1009200), the National Natural Science Foundation of China (12171069) and the Fundamental Research Funds for the Central Universities.

摘要/Abstract

摘要： This paper studies the emergent dynamics of a flock with nonlinear inherent dynamics under closest neighbors model. We establish sufficient frameworks for convergence to flocking in terms of initial state and system parameters. When the number of closest neighbors is at least half of the population, it is shown that convergence to flocking occurs regardless of the initial state provided that the Lipschitz constant of nonlinear dynamics is smaller than the coupling strength. In contrast, when this number of closest neighbors is less than half of the population, we need to impose some restrictive conditions on the initial state to ensure the emergence of flocking based on the disturbed graphs approach. Our results are applicable to both continuous and discrete time cases. Finally, the validity of our theoretical analysis is tested by numerical simulations.

关键词: multi-agent systems, flocking, closest neighbors, internal dynamics

Abstract: This paper studies the emergent dynamics of a flock with nonlinear inherent dynamics under closest neighbors model. We establish sufficient frameworks for convergence to flocking in terms of initial state and system parameters. When the number of closest neighbors is at least half of the population, it is shown that convergence to flocking occurs regardless of the initial state provided that the Lipschitz constant of nonlinear dynamics is smaller than the coupling strength. In contrast, when this number of closest neighbors is less than half of the population, we need to impose some restrictive conditions on the initial state to ensure the emergence of flocking based on the disturbed graphs approach. Our results are applicable to both continuous and discrete time cases. Finally, the validity of our theoretical analysis is tested by numerical simulations.

Key words: multi-agent systems, flocking, closest neighbors, internal dynamics

Yuan LIANG, Chen WU, Jiugang DONG. EMERGENT BEHAVIOR OF CLOSEST NEIGHBORS MODEL WITH NONLINEAR INHERENT DYNAMICS[J]. 数学物理学报(英文版), 2025, 45(4): 1640-1658.

Yuan LIANG, Chen WU, Jiugang DONG. EMERGENT BEHAVIOR OF CLOSEST NEIGHBORS MODEL WITH NONLINEAR INHERENT DYNAMICS[J]. Acta mathematica scientia,Series B, 2025, 45(4): 1640-1658.

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EMERGENT BEHAVIOR OF CLOSEST NEIGHBORS MODEL WITH NONLINEAR INHERENT DYNAMICS

EMERGENT BEHAVIOR OF CLOSEST NEIGHBORS MODEL WITH NONLINEAR INHERENT DYNAMICS

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