Entr\'ee-sortie dans le halo d'une courbe lente semi-stable

TL;DR

This paper investigates slow-fast differential systems in population dynamics, demonstrating the existence of special solutions called canards that elucidate stability properties as the period grows large.

Contribution

It establishes the existence of canard solutions along semi-stable slow curves in a two-dimensional slow-fast system, linking these to stability in linear models with periodic coefficients.

Findings

Existence of canard solutions along semi-stable slow curves.

Connection between canards and stability properties in population models.

Insights into the behavior of linear models with periodic coefficients.

Abstract

We consider a slow-fast differential system (SF) in dimension two which appears in the study of some linear model (LM) with periodic coefficients in population dynamics. We show existence of "canard solutions" of (SF) along semi-stable slow curve which explains some stability properties of (LM) when the period tends to infinity.