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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2503.12980 |
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| _version_ | 1866912792432345088 |
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| author | Menci, Marta Paul, Thierry Rossi, Stefano Tenna, Tommaso |
| author_facet | Menci, Marta Paul, Thierry Rossi, Stefano Tenna, Tommaso |
| contents | In this paper, we propose a numerical investigation of topological interactions in flocking dynamics. Starting from a microscopic description of the phenomena, mesoscopic and macroscopic models have been previously derived under specific assumptions. We explore the role of topological interactions by describing the convergence speed to consensus in both microscopic and macroscopic dynamics, considering different forms of topological interactions. Additionally, we compare mesoscopic and macroscopic dynamics for monokinetic and non-monokinetic initial data. Finally, we illustrate with some simulations in one- and two-dimensional domains the sensitive dependence of solutions on initial conditions, including the case where the system exhibits two solutions starting with the same initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_12980 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Numerical modeling of flocking dynamics with topological interactions Menci, Marta Paul, Thierry Rossi, Stefano Tenna, Tommaso Analysis of PDEs In this paper, we propose a numerical investigation of topological interactions in flocking dynamics. Starting from a microscopic description of the phenomena, mesoscopic and macroscopic models have been previously derived under specific assumptions. We explore the role of topological interactions by describing the convergence speed to consensus in both microscopic and macroscopic dynamics, considering different forms of topological interactions. Additionally, we compare mesoscopic and macroscopic dynamics for monokinetic and non-monokinetic initial data. Finally, we illustrate with some simulations in one- and two-dimensional domains the sensitive dependence of solutions on initial conditions, including the case where the system exhibits two solutions starting with the same initial data. |
| title | Numerical modeling of flocking dynamics with topological interactions |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.12980 |