Stochastic bifurcation in a driven laser system

Experiment and theory

Lora Billings, Ira B. Schwartz, David S. Morgan, Erik M. Bollt, Riccardo Meucci, Enrico Allaria

Research output: Contribution to journalArticleResearchpeer-review

13 Citations (Scopus)

Abstract

We analyze the effects of stochastic perturbations in a physical example occurring as a higher-dimensional dynamical system. The physical model is that of a class-[Formula presented] laser, which is perturbed stochastically with finite noise. The effect of the noise perturbations on the dynamics is shown to change the qualitative nature of the dynamics experimentally from a stochastic periodic attractor to one of chaoslike behavior, or noise-induced chaos. To analyze the qualitative change, we apply the technique of the stochastic Frobenius-Perron operator [L. Billings, Phys. Rev. Lett. 88, 234101 (2002)] to a model of the experimental system. Our main result is the identification of a global mechanism to induce chaoslike behavior by adding stochastic perturbations in a realistic model system of an optics experiment. In quantifying the stochastic bifurcation, we have computed a transition matrix describing the probability of transport from one region of phase space to another, which approximates the stochastic Frobenius-Perron operator. This mechanism depends on both the standard deviation of the noise and the global topology of the system. Our result pinpoints regions of stochastic transport whereby topological deterministic dynamics subjected to sufficient noise results in noise-induced chaos in both theory and experiment.

Original languageEnglish
Number of pages1
JournalPhysical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics
Volume70
Issue number2
DOIs
StatePublished - 1 Jan 2004

Fingerprint

Stochastic Bifurcation
Frobenius-Perron Operator
Laser
Stochastic Perturbation
lasers
Experiment
Chaos
perturbation
chaos
Transition Matrix
Physical Model
Standard deviation
Attractor
Optics
operators
Phase Space
High-dimensional
Dynamical system
Sufficient
Topology

Cite this

Billings, Lora ; Schwartz, Ira B. ; Morgan, David S. ; Bollt, Erik M. ; Meucci, Riccardo ; Allaria, Enrico. / Stochastic bifurcation in a driven laser system : Experiment and theory. In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics. 2004 ; Vol. 70, No. 2.
@article{23a1e62d76714525af33b0cbdc35343e,
title = "Stochastic bifurcation in a driven laser system: Experiment and theory",
abstract = "We analyze the effects of stochastic perturbations in a physical example occurring as a higher-dimensional dynamical system. The physical model is that of a class-[Formula presented] laser, which is perturbed stochastically with finite noise. The effect of the noise perturbations on the dynamics is shown to change the qualitative nature of the dynamics experimentally from a stochastic periodic attractor to one of chaoslike behavior, or noise-induced chaos. To analyze the qualitative change, we apply the technique of the stochastic Frobenius-Perron operator [L. Billings, Phys. Rev. Lett. 88, 234101 (2002)] to a model of the experimental system. Our main result is the identification of a global mechanism to induce chaoslike behavior by adding stochastic perturbations in a realistic model system of an optics experiment. In quantifying the stochastic bifurcation, we have computed a transition matrix describing the probability of transport from one region of phase space to another, which approximates the stochastic Frobenius-Perron operator. This mechanism depends on both the standard deviation of the noise and the global topology of the system. Our result pinpoints regions of stochastic transport whereby topological deterministic dynamics subjected to sufficient noise results in noise-induced chaos in both theory and experiment.",
author = "Lora Billings and Schwartz, {Ira B.} and Morgan, {David S.} and Bollt, {Erik M.} and Riccardo Meucci and Enrico Allaria",
year = "2004",
month = "1",
day = "1",
doi = "10.1103/PhysRevE.70.026220",
language = "English",
volume = "70",
journal = "Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics",
issn = "1063-651X",
publisher = "American Physical Society",
number = "2",

}

Stochastic bifurcation in a driven laser system : Experiment and theory. / Billings, Lora; Schwartz, Ira B.; Morgan, David S.; Bollt, Erik M.; Meucci, Riccardo; Allaria, Enrico.

In: Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics, Vol. 70, No. 2, 01.01.2004.

Research output: Contribution to journalArticleResearchpeer-review

TY - JOUR

T1 - Stochastic bifurcation in a driven laser system

T2 - Experiment and theory

AU - Billings, Lora

AU - Schwartz, Ira B.

AU - Morgan, David S.

AU - Bollt, Erik M.

AU - Meucci, Riccardo

AU - Allaria, Enrico

PY - 2004/1/1

Y1 - 2004/1/1

N2 - We analyze the effects of stochastic perturbations in a physical example occurring as a higher-dimensional dynamical system. The physical model is that of a class-[Formula presented] laser, which is perturbed stochastically with finite noise. The effect of the noise perturbations on the dynamics is shown to change the qualitative nature of the dynamics experimentally from a stochastic periodic attractor to one of chaoslike behavior, or noise-induced chaos. To analyze the qualitative change, we apply the technique of the stochastic Frobenius-Perron operator [L. Billings, Phys. Rev. Lett. 88, 234101 (2002)] to a model of the experimental system. Our main result is the identification of a global mechanism to induce chaoslike behavior by adding stochastic perturbations in a realistic model system of an optics experiment. In quantifying the stochastic bifurcation, we have computed a transition matrix describing the probability of transport from one region of phase space to another, which approximates the stochastic Frobenius-Perron operator. This mechanism depends on both the standard deviation of the noise and the global topology of the system. Our result pinpoints regions of stochastic transport whereby topological deterministic dynamics subjected to sufficient noise results in noise-induced chaos in both theory and experiment.

AB - We analyze the effects of stochastic perturbations in a physical example occurring as a higher-dimensional dynamical system. The physical model is that of a class-[Formula presented] laser, which is perturbed stochastically with finite noise. The effect of the noise perturbations on the dynamics is shown to change the qualitative nature of the dynamics experimentally from a stochastic periodic attractor to one of chaoslike behavior, or noise-induced chaos. To analyze the qualitative change, we apply the technique of the stochastic Frobenius-Perron operator [L. Billings, Phys. Rev. Lett. 88, 234101 (2002)] to a model of the experimental system. Our main result is the identification of a global mechanism to induce chaoslike behavior by adding stochastic perturbations in a realistic model system of an optics experiment. In quantifying the stochastic bifurcation, we have computed a transition matrix describing the probability of transport from one region of phase space to another, which approximates the stochastic Frobenius-Perron operator. This mechanism depends on both the standard deviation of the noise and the global topology of the system. Our result pinpoints regions of stochastic transport whereby topological deterministic dynamics subjected to sufficient noise results in noise-induced chaos in both theory and experiment.

UR - http://www.scopus.com/inward/record.url?scp=85036424946&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.70.026220

DO - 10.1103/PhysRevE.70.026220

M3 - Article

VL - 70

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 2

ER -