I'm looking to compute the global stable and unstable manifolds for the equilibrium points of the following autonomous vector field on the plane. Apologies for the formatting, I haven't figured out MathJax yet.
x'= -x
y'= y - y^4
For x and y in the Real numbers
So far I've computed the equilibrium points at (0,0) and (0,1) and their linear stability as a saddle point and a sink respectively.
I'm not sure how to continue with the question and would appreciate any pointers.