  A model to simulate the phenomenon of random lasing is presented. It couples
Maxwell's equations with the rate equations of electronic population in a
disordered system. Finite difference time domain methods are used to obtain the
field pattern and the spectra of localized lasing modes inside the system. A
critical pumping rate $P_{r}^{c}$ exists for the appearance of the lasing
peaks. The number of lasing modes increase with the pumping rate and the length
of the system. There is a lasing mode repulsion. This property leads to a
saturation of the number of modes for a given size system and a relation
between the localization length $\xi$ and average mode length $L_m$.
