Multistabilities and anomalous switching in the Lorenz-Haken model

We show that pulses in the Lorenz-Haken model can be observed well below the well-known second threshold by using the anomalous switching technique. More specifically, if the laser system initially operates stably above the first threshold, the pulse motion can be set in when we abruptly switch the pump to a new value, which is much smaller than the second threshold. This phenomenon is due to the existence of multistable attractors and anomalous switching between these attractors. By using the anomalous switching, three physically distinguishable attractors, namely, two time-dependent and one stationary, are numerically shown to coexist for some parameters.