x9 − 2s y 2 1d 2 asx 2 1d, y9 − 2s y 2 1d 2 1

a sx 2 1d, a ± 21, 0, 1, x, y . 0 A system of differential equations is given.

(a) Use a phase plane analysis to determine the values of the constant a for which the sole equilibrium of the differential equations is locally stable.

(b) Obtain an expression for each equilibrium (it may be a function of the constant a).