We consider the classical Lotka-Volterra prey-predator model, where a control can act on the predators in terms of a mortality term. The objective is to protect the preys, maintaining their density above a given threshold with the help of the control.
State variables
- $x$ : the preys
- $y$ : the predators
Control variables:
$u$ : the mortality term of the predators
Dynamics
$$\left\{\begin{array}{l}x'=x*(r-y)\\ y'=y*(x-m-u)\\ u\in [0;u_{\max}]\end{array}\right.$$
Dynamics parameters : $r$, $m$ and $u_{\max}$.
Constraint set
$$x>=\bar{x}$$
State domain definition
$$\left\{\begin{array}{l}x\geq 0\\y\geq 0\end{array}\right.$$
Parameter values
$r=1$, $m=1$, $u_{\max}=0.5$ and $\bar{x}=0.8$.
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