Dynamic saddle-node bifurcation in a class of slow and fast predator-prey models

Hafida Boudjellaba (1) , Tewfik Sari (2, 3)

1 Department of Mathematics and Computer Science [Laurentian Univ.]
2 LMIA - Laboratoire de Mathématiques Informatique et Applications [UHA]
3 MERE - Water Resource Modeling

We study the stability loss delay phenomenon in the dynamic saddle-node bifurcation in a class of three-dimensional prey and predator systems. The dynamics of the predator is assumed to be slow comparatively to the dynamics of the preys. As an application, a well-known model considered by Clark will be discussed.

Mots clés: Asymptotic stability; Delayed loss of stability; Singular perturbations; Canards; Biological models.; Biological models

Domaines: Systèmes dynamiques [math.DS]

Hafida Boudjellaba, Tewfik Sari. Dynamic saddle-node bifurcation in a class of slow and fast predator-prey models. 2008. ⟨hal-00270315⟩