In this example, we used lotka-volterra equations to model populations of rabbits and wolves. let's modify those equations as follows: dr dt = 0.08r(1 − 0.0002r) − 0.001rw dw dt = −0.02w + 0.00002rw. (a) according to these equations, what happens to the rabbit population in the absence of wolves? in the absence of wolves, we would expect the rabbit population to stabilize a

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.