Curvature in chemotaxis: A model for ant trail pattern formation - Centre de mathématiques appliquées (CMAP)
Pré-Publication, Document De Travail Année : 2024

Curvature in chemotaxis: A model for ant trail pattern formation

Résumé

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.
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Dates et versions

hal-04676778 , version 1 (26-08-2024)
hal-04676778 , version 2 (30-09-2024)

Identifiants

  • HAL Id : hal-04676778 , version 2

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Charles Bertucci, Matthias Rakotomalala, Milica Tomasevic. Curvature in chemotaxis: A model for ant trail pattern formation. 2024. ⟨hal-04676778v2⟩
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