About viability and minimal time crisis problem for the Lotka-Volterra prey-predator model

Térence Bayen (1) , Alain Rapaport (2, 3)

1 IMAG - Institut Montpelliérain Alexander Grothendieck
2 INRA - Institut National de la Recherche Agronomique
3 MISTEA - Mathématiques, Informatique et STatistique pour l'Environnement et l'Agronomie

We study the minimal time crisis problem for the classical Lotka-Volterra prey-predator model. Our aim is to maintain the system in a subset K for which the number of preys is above a given threshold. In the case where the viability kernel of K is non-empty, we provide an analytic description of this set and compute the minimal time function steering the system to this set. We compare this strategy with the minimal time crisis function that is computed numerically via a regularization method. We also investigate the minimal time crisis problem numerically in the case where the viability kernel is empty.

Mots clés: Optimal control; prey-predator model; Pontryagin Maximum Principle

Domaines: Mathématiques [math]

Térence Bayen, Alain Rapaport. About viability and minimal time crisis problem for the Lotka-Volterra prey-predator model . 2016. ⟨hal-01369371v2⟩