  We study the dynamical evolution of strongly coupled field theories,
initially in thermal equilibrium, under the influence of an external driving
force. We model the field theory holographically using classical gravitational
dynamics in an asymptotically AdS spacetime. The system is driven by a source
for a (composite) scalar operator. We focus on a scenario where the external
source is periodic in time and chart out the response of several observables.
We find an interesting phase structure in the response as a function of the
amplitude of the source and driving frequency. Specifically the system
transitions from a dissipation dominated phase, via a dynamical crossover to a
highly resonant amplification phase. The diagnostics of these phases include
the response of the operator in question, entropy production, energy
fluctuations, and the temporal change of entanglement entropy for small
subsystems. We comment on evidence for a potential phase transition in the
energy fluctuations of the system.
