# Steady states/systems of differential equations/Phase portraits !

1. May 18, 2012

### sid9221

http://dl.dropbox.com/u/33103477/2007%2010b.png [Broken]

I'm can't get my head around this question, there doesn't seem to be enough information to compute a steady state ?

Any idea's on how to begin ??

Last edited by a moderator: May 6, 2017
2. May 18, 2012

### spamiam

Hi sid9221,

First of all, can't you solve explicitly for p(t) and r(t)? The ODE for r(t) should look very familiar.

This problem seems a bit strange. Typically to find the steady states you set $\frac{dp}{dt} = 0$ and $\frac{dr}{dt} = 0$. These two conditions give you steady states $(p_*, r_*)$. What do you get in this case?

It seems very fishy to me that $\frac{dp}{dt}$ and $\frac{dr}{dt}$ don't seem to depend on p at all...

Could we see part a) of the question, too?

3. May 18, 2012

### sid9221

Part a) is completely unrelated.

It's some nonsense about the population of fish....

4. May 18, 2012

### spamiam

The situations may be different, but are the models similar?

Did you solve for p(t) and r(t) or find the condition given by setting the derivatives to zero?

5. May 18, 2012

### sid9221

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

Last edited by a moderator: May 6, 2017
6. May 18, 2012

### spamiam

Thanks for posting the full problem.

Anyway, if you set $\frac{dp}{dt}=0$ and $\frac{dr}{dt} = 0$, what must r equal?

Also, if $r'(t) = - \beta \, r(t)$, what function must $r(t)$ be?