Infinite primary saddle-node bifurcation in periodically forced systems - Schwartz, Ira B. (Physics letters. A, 1988)
In many physical systems subject to periodic stimuli, it is observed that as the drive amplitude is increased, chaotic oscillations emanate from subharmonic orbits of period 2πn Ω where n is a positive integer, and Ω is the drive frequency. These subharmonic orbits appear as primary (or first) saddle-node bifurcations (PSNB) and do not necessarily stem from the creation of a topological horseshoe. Rather, they can be created from perturbations of periodic orbits of an nondriven conservative system. Here, it is shown for a model of a periodically driven laser how the PSNB come into existence. As a result of the existence of PSNB, as the damping parameter is varied, there exist isolated closed bifurcation curves consisting of saddle-node pairs.