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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)
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