The dynamics of an electron moving in the Coulomb field of a nucleus and a strong periodic field is studied in a semiclassical model. Hamiltonian equations of motion are derived using Gaussian wave functions, a variational principle, and an adiabatic approximation for the width of the wave packets. Predictions for the ionization probability are found to agree rather well with exact calculations in the barrier suppression regime. By introducing dissipation and fluctuation the model atom is considered as an open system. For the dissipative system we investigate the bifurcations in dependence on strength and frequency of the external field. A quite complex bifurcation scenario is obtained. The sensitivity with respect to noise is also studied.