SILNIKOV-SADDLE-NODE INTERACTION NEAR A CODIMENSION-2 BIFURCATION - LASER WITH INJECTED SIGNAL

We describe a Sil'nikov-saddle-node interaction in the proximity of a Hopf-saddle-node bifurcation both from numerical and theoretical viewp oints, inspired by numerical observations on a three-dimensional model of a laser with injected signal. We describe the interaction near the codimension-2 point using a return map controlled by the parameters o f the bifurcation. The theoretical predictions compare well with numer ical experiments. Finally, we discuss the reasons for the existence of the Sil'nikov-saddle-node bifurcation in the laser with injected sign al, and correspondingly, the characteristics of other systems that mig ht display this bifurcation.