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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2601.16820 |
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| _version_ | 1866918302231560192 |
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| author | Rakotomalala, Matthias de Wit, Oscar |
| author_facet | Rakotomalala, Matthias de Wit, Oscar |
| contents | This paper studies the existence of multiple non-trivial stationary solutions of a partial differential equation (PDE) model introduced in [3], motivated by collective ant behavior. Previous work suggested the presence of two types of non-trivial stationary solutions for this PDE system: spot and lane solutions. In this paper, we establish the existence of these families of solutions along a bifurcation sequence as the interaction strength grows, with progressively increasing numbers of clusters and parallel lanes, respectively. Finally, we show that, for small values of the anticipation parameter, the first bifurcating spot solutions are locally dynamically stable, while the lane solutions are unstable. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_16820 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Existence of spot and lane stationary solutions for an ant active matter PDE model Rakotomalala, Matthias de Wit, Oscar Analysis of PDEs This paper studies the existence of multiple non-trivial stationary solutions of a partial differential equation (PDE) model introduced in [3], motivated by collective ant behavior. Previous work suggested the presence of two types of non-trivial stationary solutions for this PDE system: spot and lane solutions. In this paper, we establish the existence of these families of solutions along a bifurcation sequence as the interaction strength grows, with progressively increasing numbers of clusters and parallel lanes, respectively. Finally, we show that, for small values of the anticipation parameter, the first bifurcating spot solutions are locally dynamically stable, while the lane solutions are unstable. |
| title | Existence of spot and lane stationary solutions for an ant active matter PDE model |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2601.16820 |