Vol. 3, No. 3, 2010

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ISSN: 1944-4184 (e-only)
ISSN: 1944-4176 (print)
Coexistence of stable ECM solutions in the Lang–Kobayashi system

Ericka Mochan, C. Davis Buenger and Tamas Wiandt

Vol. 3 (2010), No. 3, 259–271
Abstract

The Lang–Kobayashi system of delay differential equations describes the behavior of the complex electric field and inversion N inside an external cavity semiconductor laser. This system has a family of special periodic solutions known as external cavity modes (ECMs). It is well known that these ECM solutions appear through saddle-node bifurcations, then lose stability through a Hopf bifurcation before new ECM solutions are born through a secondary saddle-node bifurcation. Employing analytical and numerical techniques, we show that for certain short external cavity lasers the loss of stability happens only after the secondary saddle-node bifurcations, which means that stable ECM solutions can coexist in these systems. We also investigate the basins of these ECM attractors.

Keywords
delay differential equations, bifurcations, Lang–Kobayashi equations
Mathematical Subject Classification 2000
Primary: 37G35, 37M20, 78A60
Milestones
Received: 15 September 2009
Revised: 6 August 2010
Accepted: 19 August 2010
Published: 16 October 2010

Communicated by John Baxley
Authors
Ericka Mochan
Department of Biomedical Engineering
Western New England College
Springfield, MA 01119
United States
C. Davis Buenger
Department of Mathematics
The Ohio State University
Columbus, OH 43201
United States
Tamas Wiandt
School of Mathematical Sciences
Rochester Institute of Technology
Rochester, NY 14623
United States