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 language | English |
|---|---|
| Number of pages | 1 |
| Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |
| Volume | 70 |
| Issue number | 2 |
| DOIs | |
| State | Published - 1 Jan 2004 |
Fingerprint
Cite this
}
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 journal › Article › Research › peer-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 -