# Dynamics on the phase plane

The following (simplified) system of ODEs models the competition between two animal
species (rabbit and sheep)
\begin{align}
\dot{r} &= r(3-r-s),\cr
\dot{s} &= s(4-2r-s).
\end{align}
There are four fixed points, and the behaviour of the systems in the first
quadrant is determined by the special curves (separatrices, invariant manifold, ...).
You can click on the figure to see how the points move on the plane.