Curvature in chemotaxis: A model for ant trail pattern formation
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866917757514153984 |
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| author | Bertucci, Charles Rakotomalala, Matthias Tomasevic, Milica |
| author_facet | Bertucci, Charles Rakotomalala, Matthias Tomasevic, Milica |
| contents | In this paper, we propose a new model of chemotaxis motivated by ant trail pattern formation, formulated as a coupled parabolic-parabolic local PDE system, for the population density and the chemical field. The main novelty lies in the transport term of the population density, which depends on the second-order derivatives of the chemical field. This term is derived as an anticipation-reaction steering mechanism of an infinitesimally small ant as its size approaches zero. We establish global-in-time existence and uniqueness for the model, and the propagation of regularity from the initial data. Then, we build a numerical scheme and present various examples that provide hints of trail formation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2408_13363 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curvature in chemotaxis: A model for ant trail pattern formation Bertucci, Charles Rakotomalala, Matthias Tomasevic, Milica Analysis of PDEs In this paper, we propose a new model of chemotaxis motivated by ant trail pattern formation, formulated as a coupled parabolic-parabolic local PDE system, for the population density and the chemical field. The main novelty lies in the transport term of the population density, which depends on the second-order derivatives of the chemical field. This term is derived as an anticipation-reaction steering mechanism of an infinitesimally small ant as its size approaches zero. We establish global-in-time existence and uniqueness for the model, and the propagation of regularity from the initial data. Then, we build a numerical scheme and present various examples that provide hints of trail formation. |
| title | Curvature in chemotaxis: A model for ant trail pattern formation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2408.13363 |