I've got the following system of equations:
$x' = -x -2y + x^2y^2$ and $y'=x-\frac{1}{2} y - \frac{1}{2} x^3y$
I have to check whether zero solution (solution for x=y=0) is stable. Is it Lyapunov stable? Is it asymptotically stable?
Please, may somebody show me the full solution? This is the subject I have to prepare without my teacher for the exam and I would really like to have it absolutely right, from the beginning till the end.