Article Dans Une Revue Mathematical Models and Methods in Applied Sciences Année : 2025

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

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Charles Bertucci, Matthias Rakotomalala, Milica Tomašević. Curvature in chemotaxis: A model for ant trail pattern formation. Mathematical Models and Methods in Applied Sciences, 2025, 35 (12), pp.2695-2740. ⟨10.1142/S0218202525500496⟩. ⟨hal-04676778v2⟩
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