2017/03/27 by Benjamin Ambrosio, Ambrosio, B., M. A. Aziz-Alaoui +3
Environmental Science · Medicine · #Animal Ecology and Behavior Studies #Dynamical Systems (math.DS) #Ecosystem dynamics and resilience #FOS: Mathematics #Mathematical and Theoretical Epidemiology and Ecology Models
paper · pdf · doi:10.48550/arxiv.1703.09266
openalex publication_date 2017/03/27 · openalex created_date 2017/09/15 · openalex updated_date 2026/07/28
Geometrical Singular Perturbation Theory has been successful to investigate a broad range of biological problems with different time scales. The aim of this paper is to apply this theory to a predator-prey model of modified Leslie-Gower type for which we consider that prey reproduces mush faster than predators. This naturally leads to introduce a small parameter ε which gives rise to a slow-fast system. This system has a special folded singularity which has not been analyzed in the classical work of Krupa-Szmolyan. We use the blow-up technique to visualize the behavior near this fold point P. Outside of this region the dynamics are given by classical singular perturbation theory. This allows to quantify geometrically the attractive limit-cycle with an error of O(ε) and shows that it exhibits the canard phenomenon while crossing P.