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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/2602.19257 |
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| _version_ | 1866911461511528448 |
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| author | Borsotti, Jacopo Jardón-Kojakhmetov, Hildeberto Sensi, Mattia |
| author_facet | Borsotti, Jacopo Jardón-Kojakhmetov, Hildeberto Sensi, Mattia |
| contents | We study a slow-fast parasite--host model featuring a singularity at the extinction state. Using techniques from Geometric Singular Perturbation Theory (GSPT), and in particular the so-called blow-up method, we desingularize that point and reconstruct the local and global dynamics. The system we consider is in non-standard GSPT form and is characterized by a rich dynamical behavior: families of slow-fast homoclinic orbits, canard-like transitions generated by trajectories that remain close to a repelling critical manifold, and topological changes produced by infinitesimal variations of the infection rate, including the creation and destruction of an endemic equilibrium. We conclude with a numerical exploration of the model, to illustrate our analytical results. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_19257 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Slow-fast dynamics in a planar parasite--host model with an extinction singularity Borsotti, Jacopo Jardón-Kojakhmetov, Hildeberto Sensi, Mattia Dynamical Systems We study a slow-fast parasite--host model featuring a singularity at the extinction state. Using techniques from Geometric Singular Perturbation Theory (GSPT), and in particular the so-called blow-up method, we desingularize that point and reconstruct the local and global dynamics. The system we consider is in non-standard GSPT form and is characterized by a rich dynamical behavior: families of slow-fast homoclinic orbits, canard-like transitions generated by trajectories that remain close to a repelling critical manifold, and topological changes produced by infinitesimal variations of the infection rate, including the creation and destruction of an endemic equilibrium. We conclude with a numerical exploration of the model, to illustrate our analytical results. |
| title | Slow-fast dynamics in a planar parasite--host model with an extinction singularity |
| topic | Dynamical Systems |
| url | https://arxiv.org/abs/2602.19257 |