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.