The nonlinear drift-wave equation driven by a sinusoidal wave is discussed in a coordinate system moving in the driving phase speed. It is shown that the hysteretic jump of the wave energy and its transition to periodic motions from the steady state can be described integrately by the perturbation method proposed in this paper. The saddle-node and Hopf bifurcations of certain resonance mode are responsible for them respectively. The frequency of the periodic oscillatory wave energy is relevant to the eigen-frequency of the system, which is different from the one in the laboratory frame due to the Doppler shift and the nonlinea-rity.