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

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Abstract
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).