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PDE1: Partial Differential Equations Location: G227 Session Chair: Simon Markfelder Session Chair: Marlies Pirner | |
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Analysis of a PDE Model for Ant Trail Patterns 1: Technical University of Munich, Germany; 2: Université Claude Bernard Lyon 1, France We present a detailed analytical study of a nonlinear PDE model for ant trail formation introduced in [Bertucci, Rakotomalala, Tomašević, 2025]. The model consists of a coupled system of two parabolic equations: one governing the pheromone field produced by the particles, and an active-matter equation describing the particle density driven by this chemical signal. A previous numerical study [Bruna, Schmidtchen, de Wit, 2025] revealed complex behavior in this model. We here provide a rigorous analysis of its dynamical and stationary properties. We establish the existence of a compact global attractor and derive a dimensional lower bound for it. We then prove the existence of families of spot and lane solutions arising along bifurcation branches as the interaction strength increases. References:
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