x9 − ax 1 x3 A differential equation is given.

(a) Determine all equilibria as a function of the constant a.

(b) Construct a phase plot and use it to determine the stability of the equilibria found in part

(a) for three different values of the constant: (i) a , 0, (ii) a − 0, and (iii) a . 0.

(c) Use the local stability criterion to verify your answers to part (b).