Resonance Structure in a Weakly detuned Laser with Injected Signal

We describe the qualitative dynamics and bifurcation set for a laser with injected signal for small cavity detunings. The main organizing center is the Hopf-saddle-node bifurcation from where a secondary Hopf bifurcation of a periodic orbit originates. We show that the laser’s stable cw solution existing for low injections, also suffers a secondary Hopf bifurcation. The resonance structure of both tori interact, and homoclinic orbits to the “off” state are found inside each Arnold tongue. The accumulation of all the above resonances towards the Hopfsaddle-node singularity points to the occurrence of a highly degenerate global bifurcation at the codimension-2 point.