### Forest model

Let us consider the age-structured forest model proposed by Antonovsky and Korzukhin (1989), defined by

\begin{equation*} \begin{cases} \dot{x} = \rho y - \gamma(y) x - f x \\ \dot{y} = f x - h y, \end{cases} \end{equation*}
where $x$ and $y$ denote the densities of young and old trees respectively, in a given forest ecosystem. The parameters $\rho$ and $h$ model the fertility of the species and the mortality of old trees respectively. The parameter $f$ models the aging rate of young trees. If $h$ increases and $\rho$ decreases, then the health of the forest is compromised.

### Simulation

$\rho =$
$h =$
$f =$ Warning! You must enter decimal numbers between $0$ and $1$.

Phase portrait of the forest model

## Bibliography

Korzukhin, MD and Antonovsky, MY. Population Level Models of Forest Dynamics, International Institute for Applied Systems Analysis, 1989.