Entry-exit in the halo of a slow semi-stable curve

TL;DR

This paper investigates slow-fast differential systems in population dynamics, demonstrating the existence of canard solutions along semi-stable slow curves that elucidate stability properties of linear models with periodic coefficients.

Contribution

It establishes the existence of canard solutions in a specific class of slow-fast systems related to population dynamics, linking these solutions to stability analysis.

Findings

Existence of canard solutions along semi-stable slow curves.

Connection between canard solutions and stability properties of linear models.

Insights into behavior of population 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.