(a) Prove that the origin of the system

˙ x = −x − y2 + xz − x3,

˙ y = −y + z2 + xy − y3,

˙z = −z + x2 + yz − z3 is globally asymptotically stable.

(b) Determine the domain of stability for the system

˙ x = −ax + xyz, ˙ y = −by + xyz, ˙z = −cz + xyz.