Solving Predator & Prey Equation: Rabbit Pop w/ No Wolves

[wallz]

i was doing some practise problems to see how much of the material i understand
well I'm having a lot of trouble with this differential equations chapter in my textbook , especially the predator and prey questions

so you have rabbits and wolves

Rabbits: dR/dt= 0.08R(1-0.0002)-0.001RW
Wolves: dW/dt= -0.02W+ 0.00002RW

The question is asking what happens to the rabbit population in the absence of wolves?

well first i just let w=0 in the rabbits equation
but then after that i had no luck, i tried the concepts i learned about separable equations however there is no t term in the equation
am i missing something? how do i go about doing this?

 

[lurflurf]

dR/dt= 0.08R(1-0.0002)-0.001RW
w->0
dR/dt= 0.08R(1-0.0002)
can you see what happens now?

you do not need t terms to separate (you will get some by integration)
dR/dt= 0.08R(1-0.0002)

dR/R= 0.08(1-0.0002)dt

 

[wallz]

OHHHHHHHH
that last part totally slipped my mind
i will try that
thank you

hmm i looked up the answer and steps were shown that i don't fully understand
after letting w=0, dR/dt=0, and the book tells me R equals 0 or 5000 then

 

[deluks917]

Something is odd about those equations. If W = 0 at any point W = 0 forever. So the equations reduce to:

dR/dt= 0.08R(1-0.0002)-0.001R(0)

dR/dt= 0.08R(1-0.0002)

 

[epenguin]

Talking about 'separable equations' is already on a too-advanced lesson for the case where either of the variables = 0. You are with one of the most elementary (and common) d.e.'s you ever have to deal with.

Intuitively also fairly obvious qualitatively what happens. If there are no predators what would happen to a rabbit population? If there are no rabbits, i.e. nothing to eat in this simple model, what would happen to a wolf population?

Also not surprising if either of them is 0 it is 0 forever.

Yes, for the general case there is a separable equation which is not that difficult.