Stability of stationary solutions to the shadow system for the activator-in
hibitor system proposed by Gierer and Meinhardt is considered in higher dim
ensional domains. It is shown that a stationary solution with minimal "ener
gy" is stable in a weak sense if the inhibitor reacts sufficiently fast, wh
ile it is unstable whenever the reaction of the inhibitor is slow. Moreover
, the loss of stability results in a Hopf bifurcation.