Bi-instability and the global role of unstable resonant orbits in a driven laser

Thomas W. Carr, Lora Billings, Ira B. Schwartz, Ioanna Triandaf

Research output: Contribution to journalArticleResearchpeer-review

36 Citations (Scopus)

Abstract

Driven class-B lasers are devices which possess quadratic nonlinearities and are known to exhibit chaotic behavior. We describe the onset of global heteroclinic connections which give rise to chaotic saddles. These form the precursor topology which creates both localized homoclinic chaos, as well as global mixed-mode heteroclinic chaos. To locate the relevant periodic orbits creating the precursor topology, approximate maps are derived using matched asymptotic expansions and subharmonic Melnikov theory. Locating the relevant unstable fixed points of the maps provides an organizing framework to understand the global dynamics and chaos exhibited by the laser.

Original languageEnglish
Pages (from-to)59-82
Number of pages24
JournalPhysica D: Nonlinear Phenomena
Volume147
Issue number1-2
DOIs
StatePublished - 1 Dec 2000

Fingerprint

chaos
orbits
topology
lasers
saddles
organizing
nonlinearity
expansion

Keywords

  • 05.45
  • Bi-instability
  • Chaos
  • Heteroclinic
  • Resonance
  • Saddle-bifurcations

Cite this

Carr, Thomas W. ; Billings, Lora ; Schwartz, Ira B. ; Triandaf, Ioanna. / Bi-instability and the global role of unstable resonant orbits in a driven laser. In: Physica D: Nonlinear Phenomena. 2000 ; Vol. 147, No. 1-2. pp. 59-82.
@article{ba2d5033f8ed499a90fd7390e60cc994,
title = "Bi-instability and the global role of unstable resonant orbits in a driven laser",
abstract = "Driven class-B lasers are devices which possess quadratic nonlinearities and are known to exhibit chaotic behavior. We describe the onset of global heteroclinic connections which give rise to chaotic saddles. These form the precursor topology which creates both localized homoclinic chaos, as well as global mixed-mode heteroclinic chaos. To locate the relevant periodic orbits creating the precursor topology, approximate maps are derived using matched asymptotic expansions and subharmonic Melnikov theory. Locating the relevant unstable fixed points of the maps provides an organizing framework to understand the global dynamics and chaos exhibited by the laser.",
keywords = "05.45, Bi-instability, Chaos, Heteroclinic, Resonance, Saddle-bifurcations",
author = "Carr, {Thomas W.} and Lora Billings and Schwartz, {Ira B.} and Ioanna Triandaf",
year = "2000",
month = "12",
day = "1",
doi = "10.1016/S0167-2789(00)00164-0",
language = "English",
volume = "147",
pages = "59--82",
journal = "Physica D: Nonlinear Phenomena",
issn = "0167-2789",
publisher = "Elsevier",
number = "1-2",

}

Bi-instability and the global role of unstable resonant orbits in a driven laser. / Carr, Thomas W.; Billings, Lora; Schwartz, Ira B.; Triandaf, Ioanna.

In: Physica D: Nonlinear Phenomena, Vol. 147, No. 1-2, 01.12.2000, p. 59-82.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Bi-instability and the global role of unstable resonant orbits in a driven laser

AU - Carr, Thomas W.

AU - Billings, Lora

AU - Schwartz, Ira B.

AU - Triandaf, Ioanna

PY - 2000/12/1

Y1 - 2000/12/1

N2 - Driven class-B lasers are devices which possess quadratic nonlinearities and are known to exhibit chaotic behavior. We describe the onset of global heteroclinic connections which give rise to chaotic saddles. These form the precursor topology which creates both localized homoclinic chaos, as well as global mixed-mode heteroclinic chaos. To locate the relevant periodic orbits creating the precursor topology, approximate maps are derived using matched asymptotic expansions and subharmonic Melnikov theory. Locating the relevant unstable fixed points of the maps provides an organizing framework to understand the global dynamics and chaos exhibited by the laser.

AB - Driven class-B lasers are devices which possess quadratic nonlinearities and are known to exhibit chaotic behavior. We describe the onset of global heteroclinic connections which give rise to chaotic saddles. These form the precursor topology which creates both localized homoclinic chaos, as well as global mixed-mode heteroclinic chaos. To locate the relevant periodic orbits creating the precursor topology, approximate maps are derived using matched asymptotic expansions and subharmonic Melnikov theory. Locating the relevant unstable fixed points of the maps provides an organizing framework to understand the global dynamics and chaos exhibited by the laser.

KW - 05.45

KW - Bi-instability

KW - Chaos

KW - Heteroclinic

KW - Resonance

KW - Saddle-bifurcations

UR - http://www.scopus.com/inward/record.url?scp=0039741988&partnerID=8YFLogxK

U2 - 10.1016/S0167-2789(00)00164-0

DO - 10.1016/S0167-2789(00)00164-0

M3 - Article

VL - 147

SP - 59

EP - 82

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 1-2

ER -