Answer:
Wolves absence would lead the rabbit population to become stable at 5,000.
Explanation:
Step 1. Concept
If there is a missing variable that should be in the system, set that particular variable to zero and make the necessary conclusion.
Step 2. Given,
dR/dt = 0.08R(1 - 000.2R) - 0.001RW
dW/dt = −0.02W + 0.00002RW
Step 3. Calculation
The transformed equations of populations of rabbit and wolves will be
dR/dt = 0.08R(1 - 000.2R) - 0.001RW
dW/dt = −0.02W + 0.00002RW
Let's check the rabbit population in the absence of wolves(W) to 0
Thus,
Differential equation dR/dt
dR/dt = 0.08R(1 - 000.2R) - 0.001RW
Take W to equal to O
dR/dt = 0.08R(1 - 000.2R) - 0.001R(0)
dR/dt = 0.08R(1 - 000.2R)
When,
dR/dt = 0 we have R = 0 or R = 5,000
This,
R = 5,000 becomes the equilibrium point in the absence of wolves
Then,
0 < R < 5,000, dR/dt > 0
For R, let's estimate a value rise of the rabbit population to 5,000
Then,
R > 5,000, dR/dt < 0
Judging from the value if R, we infer a deduction in the rabbit population by 5,000
Thus,
We can conclude that wolves absence would lead the rabbit population to become stable at 5,000.
