can someone help me find/ draw the phase portraits of these two differential equations:

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can someone help me find/ draw the phase portraits of these two differential equations:

Mathematics
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For an autonomous equation like this one, the first thing to do is determine where the derivative \(\dfrac{dN}{dt}\) disappears - these are your equilibrium points. This clearly happens when either of the following equations hold: \[\begin{cases} rN=0\\[1ex] 1-\dfrac{N}{K}=0\\[1ex] \dfrac{N}{A}-1=0 \end{cases}\]

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Easy enough: the equilibrium points occur for \(N=0,K,A\). Do you have any facts about \(K\) and \(A\)? I assume they're constants, but do you know anything about their relative values? Are they both positive/negative? Is one larger than the other? etc
@SithsAndGiggles heres a picture of the assignment if it make any difference. I have completed everything except #3
So is it \(\dfrac{N}{A}\) or \(\dfrac{A}{N}\)? Your images conflict, but I assume it's the first judging by this wiki page: https://en.wikipedia.org/wiki/Allee_effect#Mathematical_models
Anyway, yes, both \(A\) and \(K\) are constants, and we assume \(00\\ y=3~~\implies~~y'>0\]You get the following phase portrait (in one dimension).|dw:1444188255191:dw|
Its the first one, but the questions is to show that this equation has the same phase portrait as the equation from wiki
Here are some sample solutions for the example.|dw:1444188408781:dw|
|dw:1444189228506:dw| would it look like this
You have three equilibrium points, and so there are four intervals you should be considering: (1) \(y>K\), (2) \(A
Sorry, replace \(y\) with \(N\) in that last comment. So let's say \(N<0\), in particular \(N=-1\). Then \[\frac{dN}{dt}=r(-1)\left( -\frac{1}{A}-1\right)\left(1+\frac{1}{K}\right)\] It looks like \(r\) is a positive constant, so keep that in mind. Since \(A\) is a positive number, the term \(-\dfrac{1}{A}-1\) is also negative. This multiplied by \(-1\) gives a positive number. Multiplied by \(r\), it's still positive. And since \(K>0\), \(1+\dfrac{1}{K}\) is too, and positive times positive is positive. Now let's say \(0
You do the same sort of thing with the other intervals. Pick a convenient test point and check the sign of the derivative. For \(AK\) I would use \(N=2K\).

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