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1. (20 points) Consider the predator-prey system
dr
dt 1)
20
(a) Find the nullclines of the system.
X-mullclines X-120 or 5-x- X
x=1 or y=x (5-x) 6
y-nullclines dy = 0 ⇒ y=0 or 1-= dt =0
y=0 y = x-1
(b) Find all equilibrium points of this system.
уû
1x=1
y=x-1
(0,0)
(-3,-4)
(1,0)
(2,1)
(2,1)
y=0
(0,0)
(5,0)
(5,0)
(1,0)
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