  In this paper we investigate the occurrence of quantum phase transitions in
topological systems out of equi- librium. More specifically, we consider
graphene with a sizable spin-orbit coupling, irradiated by circularly-
polarized light. In the absence of light, the spin-orbit coupling drives a
quantum spin Hall phase where edge currents with opposite spins
counter-propagate. On the other hand, the light generates a time-dependent
vector potential, which leads to a hopping parameter with staggered
time-dependent phases around the benzene ring. The model is a dynamical version
of the Haldane model, which considers a static staggered flux with zero total
flux through each plaquette. Since the light breaks time-reversal symmetry, a
quantum Hall phase protected by an integer topological invariant arises. By
numerically solving the complete problem, with spin-orbit coupling and light,
and investigating different values of the driving frequency {\omega}, we show
that the spectrum exhibits non-trivial gaps not only at zero energy, but also
at {\omega}/2. This additional gap is created by photon resonances between the
valence and conduction band of graphene, and the symmetry of the spectrum
forces it to lie at {\omega}/2. By increasing the intensity of the irradiation,
the topological state in the zero energy gap undergoes a dynamical phase
transition from a quantum spin Hall to a quantum Hall phase, whereas the gap
around {\omega}/2 remains in the quantum Hall regime.
