x' = y(1 + x - y(adsbygoogle = window.adsbygoogle || []).push({}); ^{2})

y' = x(1 + y - x^{2}).

C.P. => (x,y) s.t. f(x) = 0

[tex]f(x) = x' = 0 => y = 0[/tex]

[tex]f(x) = y' = 0 => x = 0[/tex]

=> (0,0) is c.p.

plug x = 0 into x':

[tex] x' = y(1 - y^{2}) => y = 0, y =\ ^{+}_{-}1 [/tex]

=> (0,1), (0,-1) are critical points.

plug y = 0 into y':

[tex] y' = x(1 - x^{2}) => x = 0, x =\ ^{+}_{-}1 [/tex]

=> (1,0), (-1,0) are critical points.

Can someone help me find the 2 critical points that I am missing?

Thanks.

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Critical points

**Physics Forums | Science Articles, Homework Help, Discussion**