http://dl.dropbox.com/u/33103477/harvesting.png [Broken]

So am I right in saying the 2 steady states are:

$$N_1=\frac{h}{r}, N_2=\frac{1-h}{\alpha}$$

Now plugging in N_1 into the equation I get:

$$\frac{-h^2 \alpha}{r} < 0$$

So N_1 is stable.

But I can't quite figure out how to classify N_2

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vela
Staff Emeritus
Homework Helper
No, that's not correct. In steady state, the population isn't changing; that is, it's when dN/dt=0.

Exactly what I was thinking, I was shying away from doing that as they did not look "pretty" and I do not know what a "harvesting term" is.

So the steady states should be:

$$N_1 = \frac{r-\sqrt{r(r-4\alpha h)}}{2ar}, N_2 = \frac{r+\sqrt{r(r-4\alpha h)}}{2ar}$$

N_1<N_2

?

vela
Staff Emeritus
Homework Helper
Yes, those are right.

The harvesting term is h. It could represent, say, the number of deer killed by hunting every year. The population is decreased by that amount every year.

How do I classify these as if I sub them back into the differential equation I get 0 ??

vela
Staff Emeritus
Homework Helper