Flocking and invariance of velocity angles
Motsch and Tadmor considered an extended Cucker-Smale model to investigate the flocking behavior of self-organized systems of interacting species. In this extended model, a cone of the vision was introduced so that outside the cone the influence of one agent on the other is lost and hence the corres...
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AIMS Press
2015-12-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2015007 |
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| author | Le Li Lihong Huang Jianhong Wu |
| author_facet | Le Li Lihong Huang Jianhong Wu |
| author_sort | Le Li |
| collection | DOAJ |
| description | Motsch and Tadmor considered an extended Cucker-Smale model to investigate the flocking behavior of self-organized systems of interacting species. In this extended model, a cone of the vision was introduced so that outside the cone the influence of one agent on the other is lost and hence the corresponding influence function takes the value zero. This creates a problem to apply the Motsch-Tadmor and Cucker-Smale method to prove the flocking property of the system. Here, we examine the variation of the velocity angles between two arbitrary agents, and obtain a monotonicity property for the maximum cone of velocity angles. This monotonicity permits us to utilize existing arguments to show the flocking property of the system under consideration, when the initial velocity angles satisfy some minor technical constraints. |
| format | Article |
| id | doaj-art-45432f994d4d42cda6a447278c9e867a |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2015-12-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-45432f994d4d42cda6a447278c9e867a2025-01-24T02:35:04ZengAIMS PressMathematical Biosciences and Engineering1551-00182015-12-0113236938010.3934/mbe.2015007Flocking and invariance of velocity anglesLe Li0Lihong Huang1Jianhong Wu2College of Mathematics and Econometrics, Hunan University, Changsha, Hunan, 410082College of Mathematics and Econometrics, Hunan University & Hunan Women's University, Changsha, Hunan, 410004Laboratory for Industrial and Applied Mathematics, Department of Mathematics and Statistics, York University, 4700 Keele Street, Toronto, ON, M3J 1P3Motsch and Tadmor considered an extended Cucker-Smale model to investigate the flocking behavior of self-organized systems of interacting species. In this extended model, a cone of the vision was introduced so that outside the cone the influence of one agent on the other is lost and hence the corresponding influence function takes the value zero. This creates a problem to apply the Motsch-Tadmor and Cucker-Smale method to prove the flocking property of the system. Here, we examine the variation of the velocity angles between two arbitrary agents, and obtain a monotonicity property for the maximum cone of velocity angles. This monotonicity permits us to utilize existing arguments to show the flocking property of the system under consideration, when the initial velocity angles satisfy some minor technical constraints.https://www.aimspress.com/article/doi/10.3934/mbe.2015007dynamic systembiomathematics.flocking |
| spellingShingle | Le Li Lihong Huang Jianhong Wu Flocking and invariance of velocity angles Mathematical Biosciences and Engineering dynamic system biomathematics. flocking |
| title | Flocking and invariance of velocity angles |
| title_full | Flocking and invariance of velocity angles |
| title_fullStr | Flocking and invariance of velocity angles |
| title_full_unstemmed | Flocking and invariance of velocity angles |
| title_short | Flocking and invariance of velocity angles |
| title_sort | flocking and invariance of velocity angles |
| topic | dynamic system biomathematics. flocking |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2015007 |
| work_keys_str_mv | AT leli flockingandinvarianceofvelocityangles AT lihonghuang flockingandinvarianceofvelocityangles AT jianhongwu flockingandinvarianceofvelocityangles |