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Main Authors: Borsotti, Jacopo, Jardón-Kojakhmetov, Hildeberto, Sensi, Mattia
Format: Preprint
Published: 2026
Subjects:
Online Access:https://arxiv.org/abs/2602.19257
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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