  We study nuclear spin dynamics in a quantum dot close to the conditions of
electron spin resonance. We show that at small frequency mismatch the nuclear
field detunes the resonance. Remarkably, at larger frequency mismatch its
effect is opposite: The nuclear system is bistable, and in one of the stable
states the field accurately tunes the electron spin splitting to resonance. In
this state the nuclear field fluctuations are strongly suppressed and nuclear
spin relaxation is accelerated.
