  We propose the dynamical stabilization of a nonequilibrium order in a driven
dissipative system comprised an atomic Bose-Einstein condensate inside a high
finesse optical cavity, pumped with an optical standing wave operating in the
regime of anomalous dispersion. When the amplitude of the pump field is
modulated close to twice the characteristic limit-cycle frequency of the
unmodulated system, a stable subharmonic response is found. The dynamical phase
diagram shows that this subharmonic response occurs in a region expanded with
respect to that where stable limit-cycle dynamics occurs for the unmodulated
system. In turning on the modulation we tune the atom-cavity system from a
continuous to a discrete time crystal.
