Hey guys, I'm suppose to find the equilibrium points of

>>305235
Sorry thought I rotated the image

>>305235
You can see that (0, -1) and (-1, 0) can't be equilibrium solutions of the system if you substitute them into your system, but the other two solutions are correct.

Instead, take it by cases that P = 0, and then P nonzero, and similarly for each of those, take the cases that Q = 0 and Q nonzero, to avoid a contradiction in your solution.

One of your missing solutions should be immediately obvious, the other will involve expressions for both P and Q in terms of alpha.

>>305305
>a contradiction in your solution
Meaning, this is why you have two points that aren't equilibrium solutions. You introduced a contradiction by your assumptions in solving both columns separately.

File: maths7.jpg (44KB, 750x658px) Image search: [Google]

44KB, 750x658px

Cheers mate

So, how's this? Guessing it's the last 4 I got?

hopeful bump

>>305571
You made an arithmetic mistake in solving for Q on the right side.
>Q(a-1) = 2
>...

There are 4 solutions. Two of your points are wrong.

You can check which ones are solutions by evaluating P' and Q' and checking that both are zero.

>>305791
ahhhh man I'm such a fool, thank you

Does anyone have an answer? I think I'm going round in circles finding the same stuff over and over again. I'm kinda slow

>>305801
np. Out of curiosity, what does it model? Competing bacterial colonies?

>>305806
(P,Q) = (0,0), (0,1/a), ((a+1)/(a-1), 2/(a-1)), (1,0)
are the solutions

>>305815
>>305815
Thank you! And it doesn't actually say, just says it's a model for two interacting populations