From the Maxwell wave equation, the beam propagation equation, which includes several nonlinear effects, such as the attachment of oxygen, was obtained. The filamentation dynamics was homologous to the problem of particles moving in a potential well. The initial conditions in which the laser beam becomes a stationary filamentation were analyzed. By the numerical simulation, the influences of beam size, power and phase on the attachment of oxygen in the filament propagation were discussed. The conclusions indicate that the power is rather consumed by the attachment of oxygen, which results in the beam size decreasing in oscillation process. The results qualitatively explain the relationship between beam size and power.