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arXiv · 2504.01765

Existence and dimensional lower bound for the global attractor of a PDE model for ant trail formation

Matthias Rakotomalala·Oscar de Wit
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Abstract

We study the asymptotic behavior of a nonlinear PDE model for ant trail formation, which was introduced in [3]. We establish the existence of a compact global attractor and prove the nonlinear instability of the homogeneous steady state under an inviscid instability condition. We also provide a dimensional lower bound on the attractor. Alternatively, we prove that if the interaction parameter is sufficiently small, the homogeneous steady state is globally asymptotically stable.

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Matthias Rakotomalala, Oscar de Wit. 2025-04-02. Existence and dimensional lower bound for the global attractor of a PDE model for ant trail formation. https://arxiv.org/abs/2504.01765

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