Question

how do you figure out the stability of a critical point from the eigenvalues of the jacobian matrix?

Answer 1

If at least of the eigenvalues is a positive real number, the equilibrium is unstable. Otherwise (if they are all negative), they are asymptotically stable, if my memory does not fail me.

Answer 2

and how do you know whether the critical point is a nodal sink or a spiral sink?

Answer 3

Check this link: http://kaharris.org/teaching/216/Lectures/lec28/lec28.pdf I think it's easier to explain with pictures :-)

Answer 4

Oh thanksss, i understand it much better now :)

Answer 5

No problem :-) Glad to be of some help.