Stability loss delay in a class of slow and fast ecological models

Hafida Boudjellaba (1) , Tewfik Sari (2)

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

We study a class of three-dimensional systems of harvesting two species. The dynamics of the harvesting effort is assumed to be slow comparatively to the dynamics of the species. By using singular perturbation theory and the stability loss delay phenomenon, we give precise conditions which guarantee the existence of a semi global asymptotically stable equilibrium. 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

Domaines: Systèmes dynamiques [math.DS]

Hafida Boudjellaba, Tewfik Sari. Stability loss delay in a class of slow and fast ecological models. 2007. ⟨hal-00163654⟩