Exercise 102

Suppose we have the predator-prey system where the foxes are also killed at a constant rate $h$ ($h$ foxes killed per unit time): $x' = (a-by)x,$ $y' = (cx-d)y - h$.

1. Find the critical points and the Jacobian matrices of the system.
2. Put in the constants $a=0.4$, $b=0.01$, $c=0.003$, $d=0.3$, $h=10$. Analyze the critical points. What do you think it says about the forest?