Stochastic bifurcation in a driven laser system: Experiment and theory

Year: 2004

Authors: Billings L., Schwartz I.B., Morgan D.S., Bollt E.M., Meucci R., Allaria E.

Autors Affiliation: Department of Mathematical Sciences, Montclair State University, Montclair, New Jersey 07043, USA;
Naval Research Laboratory, Code 6792, Plasma Physics Division, Washington, D.C. 20375, USA;
Department of Mathematics and Computer Science and Department of Physics, Clarkson University, Potsdam, New York 13699, USA;
Istituto Nazionale di Ottica Applicata, Largo E. Fermi 6, 50125 Firenze, Italy;
Department of Physics, University of Florence, Florence, Italy

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-B 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.

Journal/Review: PHYSICAL REVIEW E

Volume: 70 (2)      Pages from: 026220-1  to: 026220-10

More Information: L.B. was supported by DARPA under Grant No. DAAD19-03-1-0134. I.B.S. was supported by the Office of Naval Research and the Army Research Office. E.A. was supported by FIRB Contract No. RBAU01B49F_002.
KeyWords: Approximation theory; Bifurcation (mathematics); Gaussian noise (electronic); Hamiltonians; Natural frequencies; Perturbation techniques; Probability density function; Random processes; Vacuum; Waveform analysis, Chaotic attractors; Laser systems; Sinusoidal signals; Stochastic perturbations, Laser applications
DOI: 10.1103/PhysRevE.70.026220

Citations: 16
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