  We studied the interaction of a two-level atom with a frequency modulated
cavity mode in an ideal optical cavity. The system, described by a
Jaynes-Cumming Hamiltonian, gave rise to a set of stiff nonlinear first order
equations solved numerically using implicit and semi-implicit numerical
algorithms. We explored the evolution of the atomic system using nonlinear
dynamics tools, like time series, phase plane, power spectral density, and
Poincar\'{e} sections plots, for monochromatic and bichromatic modulations of
the cavity field. The system showed quasiperiodic and possibly chaotic behavior
when the selected monochromatic frequencies, or ratio of the bichromatic
frequencies were irrational (incommensurate) numbers. In addition, when the
modulated frequencies were overtones of the Rabi frequency of the system, a
single dominant frequency emerged for the system.
