Let R and F be the rabbit and fox populations in an ecosystem represented by the system below:

dR/dt = 0.4R 0.01RF 0.001R^2

dF/dt = 0.003RF 0.3F

1-Find the equilibrium points.

2- Linearize the system at each equilibrium, and classify the equilibrium as a sink, spiral sink, source, spiral source, saddle, or center point.

3-Sketch an approximate phase plane diagram in Quadrant I. Be sure to mark each equilibrium in your graph

4-describe the long term behavior of the rabbit and fox populations in this ecosystem.