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| Autori principali: | , |
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| Natura: | Preprint |
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2023
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| Accesso online: | https://arxiv.org/abs/2311.13238 |
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| _version_ | 1866913891142860800 |
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| author | Continelli, Elisa Pignotti, Cristina |
| author_facet | Continelli, Elisa Pignotti, Cristina |
| contents | In this paper, we analyze a Hegselmann-Krause opinion formation model and a Cucker-Smale flocking model with attractive-repulsive interaction. To be precise, we investigate the situation in which the individuals involved in an opinion formation or a flocking process attract each other in certain time intervals and repeal each other in other ones. Under quite general assumptions, we prove the convergence to consensus for the Hegselmann-Krause model and the exhibition of asymptotic flocking for the Cucker-Smale model in presence of positive-negative interaction. With some additional conditions, we are able to improve the convergence to consensus for the solutions of the Hegselmann-Krause model, namely we establish an exponential convergence to consensus result. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_13238 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Hegselmann-Krause and Cucker-Smale type models with attractive-repulsive interaction Continelli, Elisa Pignotti, Cristina Optimization and Control In this paper, we analyze a Hegselmann-Krause opinion formation model and a Cucker-Smale flocking model with attractive-repulsive interaction. To be precise, we investigate the situation in which the individuals involved in an opinion formation or a flocking process attract each other in certain time intervals and repeal each other in other ones. Under quite general assumptions, we prove the convergence to consensus for the Hegselmann-Krause model and the exhibition of asymptotic flocking for the Cucker-Smale model in presence of positive-negative interaction. With some additional conditions, we are able to improve the convergence to consensus for the solutions of the Hegselmann-Krause model, namely we establish an exponential convergence to consensus result. |
| title | Hegselmann-Krause and Cucker-Smale type models with attractive-repulsive interaction |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2311.13238 |