This study set the target to systemize the roller drafting operation and performed the characteristic analysis by simulation of the effect of the draft ratio, an important process variable, on the output sliver thickness, based on the bundle flow model. The simulative result showed that the output sliver thickness possesses a fixed point for a value of draft ratio in the range of the linear stability. As the draft ratio increases, the drafted sliver thickness changes in a periodical way, which corresponds to the critical case in a linearized system. Then for the further increase of the draft ratio the output sliver thickness has an initial increase of the deviation from the stationary value, which is justified for an unstable system, but when time elapses long, the increase of the amplitude is limited in a certain range, showing a closed trajectory in the phase plane. This dynamic characteristics is called the limit cycle behavior. Eventually the sliver output from the roller draft operation varies in the characteristics of the linear density for the draft ratio; a fixed point occurs, and then the fixed point disappears, as the draft ratio increases, which is a typical Hopf bifurcation phenomenon. The existence of the draft wave can be thus justified as a limit cycle behavior due to the non-linearity of the bundle flow system.