Controlling chaos may induce new attractors in an optical device

A. Gavrielides, P. M. Alsing, V. Kovanis, T. Erneux

Research output: Contribution to journalArticle

8 Citations (Scopus)

Abstract

The logistic map has been used to describe period doubling bifurcations for periodically modulated lasers. It also represents an asymptotic approximation of Ikeda's map for a passive ring cavity. Because various control methods have been used recently to stabilize branches of periodic solutions in lasers, we investigate the logistic map with a standard Ott, Grebogi and Yorke (OGY) control. We explore the structure of this map plus perturbations and find considerable modifications to its bifurcation diagram. In addition to the original fixed points, we find a new fixed point and new period doubling bifurcations. We show that for certain values of small perturbations the new fixed point of the perturbed logistic map is stable, while its original fixed point becomes unstable. Our analysis suggests that new branches of solutions may exist in lasers as a result of the feedback control.

Original languageEnglish
Pages (from-to)551-558
Number of pages8
JournalOptics Communications
Volume115
Issue number5-6
DOIs
Publication statusPublished - Apr 1 1995
Externally publishedYes

Fingerprint

Optical devices
Chaos theory
chaos
logistics
Logistics
period doubling
Lasers
lasers
perturbation
feedback control
Feedback control
diagrams
cavities
rings
approximation

ASJC Scopus subject areas

  • Physical and Theoretical Chemistry
  • Electrical and Electronic Engineering
  • Electronic, Optical and Magnetic Materials
  • Atomic and Molecular Physics, and Optics

Cite this

Gavrielides, A., Alsing, P. M., Kovanis, V., & Erneux, T. (1995). Controlling chaos may induce new attractors in an optical device. Optics Communications, 115(5-6), 551-558. https://doi.org/10.1016/0030-4018(95)00054-C

Controlling chaos may induce new attractors in an optical device. / Gavrielides, A.; Alsing, P. M.; Kovanis, V.; Erneux, T.

In: Optics Communications, Vol. 115, No. 5-6, 01.04.1995, p. 551-558.

Research output: Contribution to journalArticle

Gavrielides, A, Alsing, PM, Kovanis, V & Erneux, T 1995, 'Controlling chaos may induce new attractors in an optical device', Optics Communications, vol. 115, no. 5-6, pp. 551-558. https://doi.org/10.1016/0030-4018(95)00054-C
Gavrielides, A. ; Alsing, P. M. ; Kovanis, V. ; Erneux, T. / Controlling chaos may induce new attractors in an optical device. In: Optics Communications. 1995 ; Vol. 115, No. 5-6. pp. 551-558.
@article{845d4eaf172549099bcb6f6121c11fc6,
title = "Controlling chaos may induce new attractors in an optical device",
abstract = "The logistic map has been used to describe period doubling bifurcations for periodically modulated lasers. It also represents an asymptotic approximation of Ikeda's map for a passive ring cavity. Because various control methods have been used recently to stabilize branches of periodic solutions in lasers, we investigate the logistic map with a standard Ott, Grebogi and Yorke (OGY) control. We explore the structure of this map plus perturbations and find considerable modifications to its bifurcation diagram. In addition to the original fixed points, we find a new fixed point and new period doubling bifurcations. We show that for certain values of small perturbations the new fixed point of the perturbed logistic map is stable, while its original fixed point becomes unstable. Our analysis suggests that new branches of solutions may exist in lasers as a result of the feedback control.",
author = "A. Gavrielides and Alsing, {P. M.} and V. Kovanis and T. Erneux",
year = "1995",
month = "4",
day = "1",
doi = "10.1016/0030-4018(95)00054-C",
language = "English",
volume = "115",
pages = "551--558",
journal = "Optics Communications",
issn = "0030-4018",
publisher = "Elsevier",
number = "5-6",

}

TY - JOUR

T1 - Controlling chaos may induce new attractors in an optical device

AU - Gavrielides, A.

AU - Alsing, P. M.

AU - Kovanis, V.

AU - Erneux, T.

PY - 1995/4/1

Y1 - 1995/4/1

N2 - The logistic map has been used to describe period doubling bifurcations for periodically modulated lasers. It also represents an asymptotic approximation of Ikeda's map for a passive ring cavity. Because various control methods have been used recently to stabilize branches of periodic solutions in lasers, we investigate the logistic map with a standard Ott, Grebogi and Yorke (OGY) control. We explore the structure of this map plus perturbations and find considerable modifications to its bifurcation diagram. In addition to the original fixed points, we find a new fixed point and new period doubling bifurcations. We show that for certain values of small perturbations the new fixed point of the perturbed logistic map is stable, while its original fixed point becomes unstable. Our analysis suggests that new branches of solutions may exist in lasers as a result of the feedback control.

AB - The logistic map has been used to describe period doubling bifurcations for periodically modulated lasers. It also represents an asymptotic approximation of Ikeda's map for a passive ring cavity. Because various control methods have been used recently to stabilize branches of periodic solutions in lasers, we investigate the logistic map with a standard Ott, Grebogi and Yorke (OGY) control. We explore the structure of this map plus perturbations and find considerable modifications to its bifurcation diagram. In addition to the original fixed points, we find a new fixed point and new period doubling bifurcations. We show that for certain values of small perturbations the new fixed point of the perturbed logistic map is stable, while its original fixed point becomes unstable. Our analysis suggests that new branches of solutions may exist in lasers as a result of the feedback control.

UR - http://www.scopus.com/inward/record.url?scp=0029292652&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029292652&partnerID=8YFLogxK

U2 - 10.1016/0030-4018(95)00054-C

DO - 10.1016/0030-4018(95)00054-C

M3 - Article

VL - 115

SP - 551

EP - 558

JO - Optics Communications

JF - Optics Communications

SN - 0030-4018

IS - 5-6

ER -