Emergent behavior of Cucker–Smale model with time-varying topological structures and reaction-type delays
This paper studies the continuous Cucker–Smale model with time-varying topological structures and reaction-type delay. The goal of this paper is to establish a sufficient framework for flocking behaviors. Our method combines strict Lyapunov design with the derivation of an appropriate persistence co...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-12-01
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| Series: | Mathematical Modelling and Control |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/mmc.2022020?viewType=HTML |
| _version_ | 1828067530646749184 |
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| author | Qin Xu Xiao Wang Yicheng Liu |
| author_facet | Qin Xu Xiao Wang Yicheng Liu |
| author_sort | Qin Xu |
| collection | DOAJ |
| description | This paper studies the continuous Cucker–Smale model with time-varying topological structures and reaction-type delay. The goal of this paper is to establish a sufficient framework for flocking behaviors. Our method combines strict Lyapunov design with the derivation of an appropriate persistence condition for multi-agent systems. First, to prove that position fluctuations are uniformly bounded, a strict and trajectory-dependent Lyapunov functional is constructed via reparametrization of the time variable. Then, by constructing a global Lyapunov functional and using a novel backward-forward estimate, it is deduced that velocity fluctuations converge to zero. Finally, flocking behaviors are analyzed separately in terms of time delays and communication failures. |
| first_indexed | 2024-04-10T23:46:57Z |
| format | Article |
| id | doaj.art-66080201ac5f4bdf95ce5a21855e52ce |
| institution | Directory Open Access Journal |
| issn | 2767-8946 |
| language | English |
| last_indexed | 2024-04-10T23:46:57Z |
| publishDate | 2022-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Modelling and Control |
| spelling | doaj.art-66080201ac5f4bdf95ce5a21855e52ce2023-01-11T02:21:28ZengAIMS PressMathematical Modelling and Control2767-89462022-12-012420021810.3934/mmc.2022020Emergent behavior of Cucker–Smale model with time-varying topological structures and reaction-type delaysQin Xu 0Xiao Wang 1Yicheng Liu2Department of Mathematics, National University of Defense Technology, Changsha 410073, ChinaDepartment of Mathematics, National University of Defense Technology, Changsha 410073, ChinaDepartment of Mathematics, National University of Defense Technology, Changsha 410073, ChinaThis paper studies the continuous Cucker–Smale model with time-varying topological structures and reaction-type delay. The goal of this paper is to establish a sufficient framework for flocking behaviors. Our method combines strict Lyapunov design with the derivation of an appropriate persistence condition for multi-agent systems. First, to prove that position fluctuations are uniformly bounded, a strict and trajectory-dependent Lyapunov functional is constructed via reparametrization of the time variable. Then, by constructing a global Lyapunov functional and using a novel backward-forward estimate, it is deduced that velocity fluctuations converge to zero. Finally, flocking behaviors are analyzed separately in terms of time delays and communication failures.https://www.aimspress.com/article/doi/10.3934/mmc.2022020?viewType=HTMLcucker–smale modeltime-varying topological structurestime delayflockingpersistence of excitation |
| spellingShingle | Qin Xu Xiao Wang Yicheng Liu Emergent behavior of Cucker–Smale model with time-varying topological structures and reaction-type delays Mathematical Modelling and Control cucker–smale model time-varying topological structures time delay flocking persistence of excitation |
| title | Emergent behavior of Cucker–Smale model with time-varying topological structures and reaction-type delays |
| title_full | Emergent behavior of Cucker–Smale model with time-varying topological structures and reaction-type delays |
| title_fullStr | Emergent behavior of Cucker–Smale model with time-varying topological structures and reaction-type delays |
| title_full_unstemmed | Emergent behavior of Cucker–Smale model with time-varying topological structures and reaction-type delays |
| title_short | Emergent behavior of Cucker–Smale model with time-varying topological structures and reaction-type delays |
| title_sort | emergent behavior of cucker smale model with time varying topological structures and reaction type delays |
| topic | cucker–smale model time-varying topological structures time delay flocking persistence of excitation |
| url | https://www.aimspress.com/article/doi/10.3934/mmc.2022020?viewType=HTML |
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