Coupled Lorenz systems, cusp maps, and the lowering of the second laser threshold

We have studied the behavior of two symmetrically coupled Lorenz systems in the parameter space where the uncoupled systems correspond to the bad-cavity limit of the single-mode laser model. The differential equations show that the threshold for the appearance of a strange attractor in the coupled system drops below the uncoupled value, exhibits a minimum at {β}=0.5, and then increases rapidly as {β}{→}0.7. We have also studied the use of coupled logistic cusp maps for predicting the initial drop in the second laser threshold. The results show good qualitative agreement for low {β} values ({β}<0.25).