SUBHARMONIC-SADDLE CONNECTIONS AS A PRECURSOR TO CHAOS IN A PERIODICALLY MODULATED LASER

Abstract

We investigate the onset of chaos in a model for a periodically-forced class-B laser. By periodically modulating the laser-cavity damping rate we consider a pair of coupled nonautonomous ordinary differential equations for the laser intensity and population inversion. As the excitation is increased, the system exhibits saddle-node bifurcations to subharmonic oscillations, period-doubling bifurcations, chaos, and crises. Our investigations focus on the role of a pair of unstable orbits in the onset of the first chaotic attractor. One orbit is a subharmonic saddle while the other is a period one saddle. Upon creation of the period one saddle due to a period doubling bifurcation, its stable manifold immediately forms transverse intersections with the unstable manifold of a coexisting subharmonic saddle forming a heteroclinic crossing. These heteroclinic intersections provide a mechanism for the formation of horseshoes and the development of a chaotic attractor.