Rosenzweig-MacArthur model with variable disappearance rate

Amina Hammoum (1) , Tewfik Sari (2) , Karim Yadi (1)

1 LSDA - Laboratoire Systèmes Dynamiques et Applications
2 UMR ITAP - Technologies et Méthodes pour les Agricultures de demain

In this article, we consider a modified Rosenzweig-MacArthur model in which we take into account a general variable disappearance rate of the predator, in addition to its natural constant death rate. We show that the conditions of existence of a positive equilibrium are the same as for the Rosenzweig-MacArthur model, but those of stability are not. We define an arc of the ascending branch of the prey isocline out of which a positive equilibrium can be locally exponentially stable, and the ends of which can correspond to Hopf bifurcations. We apply our geometrical interpretation to the Bazykin's model for which the disappearance rate depends only on the predator density, and to the Variable-Territory model for which the disappearance rate depends on both densities. Theoretical predictions are illustrated by numerical simulations.

Mots clés: Rosenzweig -MacArthur model; General disappearance rate; Bazykin's model; Variable-territory model

Domaines: Mathématiques [math]

Amina Hammoum, Tewfik Sari, Karim Yadi. Rosenzweig-MacArthur model with variable disappearance rate. CARI 2022, Oct 2022, Tunis, Tunisia. ⟨hal-03712243⟩