  The microwave phonon stimulated emission (SE) has been experimentally and
numerically investigated in a nonautonomous microwave acoustic quantum
generator, called also microwave phonon laser or phaser (see previous works
arXiv:cond-mat/0303188 ; arXiv:cond-mat/0402640 ; arXiv:nlin.CG/0703050)
Phenomena of branching and long-time refractority (absence of the reaction on
the external pulses) for deterministic chaotic and regular processes of SE were
observed in experiments with various levels of electromagnetic pumping. At the
pumping level growth, the clearly depined increasing of the number of
coexisting SE states has been observed both in real physical experiments and in
computer simulations. This confirms the analytical estimations of the branching
density in the phase space. The nature of the refractority of SE pulses is
closely connected with the pointed branching and reflects the crises of strange
attractors, i.e. their collisions with unstable periodic components of the
higher branches of SE states in the nonautonomous microwave phonon laser.
