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Pré-Publication, Document De Travail Année : 2017

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

Résumé

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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Dates et versions

hal-01369371 , version 1 (20-09-2016)
hal-01369371 , version 2 (27-09-2016)
hal-01369371 , version 3 (19-04-2017)
hal-01369371 , version 4 (30-04-2017)

Identifiants

  • HAL Id : hal-01369371 , version 3

Citer

Térence Bayen, Alain Rapaport. About viability and minimal time crisis problem for the Lotka-Volterra prey-predator model . 2017. ⟨hal-01369371v3⟩
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