1. (25 points) In an isolated region of the Canadian Northwest Territories, a population of arctic wolves, z(t), and a population of silver foxes, y(t), compete for survival. (For cach population, one unit represents 100 individuals). The two species have a common. limited food supply, which consists mainly of mice. The interaction of the two species can be modeled by the following system of differential equations,

dr

dt

dy

3

1

dt

2

where the proportionality constants were obtained from observation.

(a) Find the nullclines of the system for 20 and y ≥ 0.

X-nullclims

x=0

y=-x+1

y-nullclines

y=0

y=-x+4

(b) Find all of the equilibrium solutions for z≥ 0 and y≥ 0.

(0,0) (0,34)