  We study the effect of driving a two-dimensional honeycomb system out of
equilibrium using an elliptically polarized light as a time-dependent
perturbation. In particular, we try to understand the topological phase diagram
of this driven system when the external drive is a vector potential given by
${\bf A}(t) = (A_{0x} \cos(\Omega t), A_{0y} \cos(\Omega t + \phi_0))$. These
topological phases are characterized by the Floquet Chern number which, in each
of these phases, is related to the number of robust edge modes on a nanoribbon.
We show that varying the ratio $A_{0x}/A_{0y}$ of the external drive is a
possible way to take the system from a trivial to a topological phase and vice
versa.
