  We study periodically driven scalar fields and the resulting geometries with
global AdS asymptotics. These solutions describe the strongly coupled dynamics
of dual finite-size quantum systems under a periodic driving which we interpret
as Floquet condensates. They span a continuous two-parameter space that extends
the linearized solutions on AdS. We map the regions of stability in the
solution space. In a significant portion of the unstable subspace, two very
different endpoints are reached depending upon the sign of the perturbation.
Collapse into a black hole occurs for one sign. For the opposite sign instead
one attains a regular solution with periodic modulation. We also construct
quenches where the driving frequency and amplitude are continuously varied.
Quasistatic quenches can interpolate between pure AdS and sourced solutions
with time periodic vev. By suitably choosing the quasistatic path one can
obtain boson stars dual to Floquet condensates at zero driving field. We
characterize the adiabaticity of the quenching processes. Besides, we speculate
on the possible connections of this framework with time crystals.
