Local versus nonlocal barycentric interactions in 1D agent dynamics
The mean-field dynamics of a collection of stochastic agents evolving under local and nonlocal interactions in one dimension is studied via analytically solvable models. The nonlocal interactions between agents result from $(a)$ a finite extension of the agents interaction range and $(b)$ a barycent...
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| Format: | Article |
| Language: | English |
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AIMS Press
2013-09-01
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| Series: | Mathematical Biosciences and Engineering |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.303 |
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| author | Max-Olivier Hongler Roger Filliger Olivier Gallay |
| author_facet | Max-Olivier Hongler Roger Filliger Olivier Gallay |
| author_sort | Max-Olivier Hongler |
| collection | DOAJ |
| description | The mean-field dynamics of a collection of stochastic agents evolving under local and nonlocal interactions in one dimension is studied via analytically solvable models. The nonlocal interactions between agents result from $(a)$ a finite extension of the agents interaction range and $(b)$ a barycentric modulation of the interaction strength. Our modeling framework is based on a discrete two-velocity Boltzmann dynamics which can be analytically discussed. Depending on the span and the modulation of the interaction range, we analytically observe a transition from a purely diffusive regime without definite pattern to a flocking evolution represented by a solitary wave traveling with constant velocity. |
| format | Article |
| id | doaj-art-5443ea47b55245b781d79f0b111b2f2b |
| institution | Kabale University |
| issn | 1551-0018 |
| language | English |
| publishDate | 2013-09-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | Mathematical Biosciences and Engineering |
| spelling | doaj-art-5443ea47b55245b781d79f0b111b2f2b2025-01-24T02:28:02ZengAIMS PressMathematical Biosciences and Engineering1551-00182013-09-0111230331510.3934/mbe.2014.11.303Local versus nonlocal barycentric interactions in 1D agent dynamicsMax-Olivier Hongler0Roger Filliger1Olivier Gallay2Ecole Polytechnique Fédérale de Lausanne, STI-IMT-LPM, Station 17, CH-1015 LausanneBern University of Applied Sciences, Quellgasse 21, CH-2501 BielIBM Zurich Research Laboratory, Saeumerstrasse 4, CH-8803 RueschlikonThe mean-field dynamics of a collection of stochastic agents evolving under local and nonlocal interactions in one dimension is studied via analytically solvable models. The nonlocal interactions between agents result from $(a)$ a finite extension of the agents interaction range and $(b)$ a barycentric modulation of the interaction strength. Our modeling framework is based on a discrete two-velocity Boltzmann dynamics which can be analytically discussed. Depending on the span and the modulation of the interaction range, we analytically observe a transition from a purely diffusive regime without definite pattern to a flocking evolution represented by a solitary wave traveling with constant velocity.https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.303flocking dynamics.interactive stochastic agentstransport processeskinetic theoryself-organized systems |
| spellingShingle | Max-Olivier Hongler Roger Filliger Olivier Gallay Local versus nonlocal barycentric interactions in 1D agent dynamics Mathematical Biosciences and Engineering flocking dynamics. interactive stochastic agents transport processes kinetic theory self-organized systems |
| title | Local versus nonlocal barycentric interactions in 1D agent dynamics |
| title_full | Local versus nonlocal barycentric interactions in 1D agent dynamics |
| title_fullStr | Local versus nonlocal barycentric interactions in 1D agent dynamics |
| title_full_unstemmed | Local versus nonlocal barycentric interactions in 1D agent dynamics |
| title_short | Local versus nonlocal barycentric interactions in 1D agent dynamics |
| title_sort | local versus nonlocal barycentric interactions in 1d agent dynamics |
| topic | flocking dynamics. interactive stochastic agents transport processes kinetic theory self-organized systems |
| url | https://www.aimspress.com/article/doi/10.3934/mbe.2014.11.303 |
| work_keys_str_mv | AT maxolivierhongler localversusnonlocalbarycentricinteractionsin1dagentdynamics AT rogerfilliger localversusnonlocalbarycentricinteractionsin1dagentdynamics AT oliviergallay localversusnonlocalbarycentricinteractionsin1dagentdynamics |