Infinite primary saddle-node bifurcation in periodically forced systems

• Published in: Physics letters. A Vol. 126; no. 7; pp. 411 - 418
• Main Author: Schwartz, Ira B.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 18.01.1988; Elsevier Science
• Subjects: Exact sciences and technology; Function theory, analysis; Mathematical methods in physics; Physics
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/0375-9601(88)90802-X

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.