# Viability analysis and minimal time problems for the Lotka-Volterra prey-predator model

Abstract : In this work, we consider several approaches for the control of the classical Lotka-Volterra prey-predator model. Our aim is to maintain the system in a subset $K(\ul x)$ for which the number of preys is above a given threshold $\ul x$. In the case where the viability kernel of $K(\ul x)$ is non-empty, we provide an analytic description of this set and we compute an optimal feedback control for the minimum time problem to reach this set. We also provide an optimal feedback control for the so-called {\it{time crisis problem}} (see \cite{bayen,DSP}). We point out that for a large set of initial conditions, the duration time spent outside $K(\ul x)$ by the solution of the time crisis problem is less than the one for the minimum time control problem.
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Type de document :
Pré-publication, Document de travail
2018
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https://hal.archives-ouvertes.fr/hal-01369371
Contributeur : Térence Bayen <>
Soumis le : vendredi 26 janvier 2018 - 08:44:18
Dernière modification le : lundi 11 juin 2018 - 10:46:02

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tc-lv-12-10-hal.pdf
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• HAL Id : hal-01369371, version 5

### Citation

Térence Bayen, Alain Rapaport. Viability analysis and minimal time problems for the Lotka-Volterra prey-predator model . 2018. 〈hal-01369371v5〉

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