Prove that the origin is a unique critical point of the system

˙ x = −

1 2

y(1+x)+x(1−4x2−y2), ˙ y = 2x(1+x)+y(1−4x2−y2).

Determine the stability of the origin using the Lyapunov function V (x, y) =

(1 − 4x2 − y2)2. Find +(p) for each p ∈ ℜ2. Plot a phase portrait.