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Resonance structure in a weakly detuned laser with injected signal

Mayol, Catalina; Natiello, Mario LU and Zimmermann, Martin (2001) In International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 11(10). p.2587-2605
Abstract
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 Hopf-saddle-node singularity points to the occurrence of a highly degenerate global bifurcation at the codimension-2 point.
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author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
laser with injected signal, resonance structures, global bifurcations
in
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering
volume
11
issue
10
pages
2587 - 2605
publisher
World Scientific
external identifiers
  • scopus:0035488684
ISSN
0218-1274
DOI
10.1142/S0218127401003693
language
English
LU publication?
yes
id
17c358ba-1dbe-45a9-bad9-017dd27606ae (old id 4153517)
alternative location
http://www.worldscientific.com/doi/abs/10.1142/S0218127401003693
date added to LUP
2013-11-15 20:44:44
date last changed
2018-01-07 08:45:12
@article{17c358ba-1dbe-45a9-bad9-017dd27606ae,
  abstract     = {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 Hopf-saddle-node singularity points to the occurrence of a highly degenerate global bifurcation at the codimension-2 point.},
  author       = {Mayol, Catalina and Natiello, Mario and Zimmermann, Martin},
  issn         = {0218-1274},
  keyword      = {laser with injected signal,resonance structures,global bifurcations},
  language     = {eng},
  number       = {10},
  pages        = {2587--2605},
  publisher    = {World Scientific},
  series       = {International Journal of Bifurcation and Chaos in Applied Sciences and Engineering},
  title        = {Resonance structure in a weakly detuned laser with injected signal},
  url          = {http://dx.doi.org/10.1142/S0218127401003693},
  volume       = {11},
  year         = {2001},
}