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 et al., 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.
MSU Digital Commons Citation
Billings, Lora; Schwartz, Ira; Morgan, David; Bollt, Erik; Meucci, Riccardo; and Allaria, Enrico, "Stochastic bifurcation in a driven laser system: Experiment and theory" (2004). Department of Mathematical Sciences Faculty Scholarship and Creative Works. 6.
Billings, L., Schwartz, I. B., Morgan, D. S., Bollt, E. M., Meucci, R., & Allaria, E. (2004). Stochastic bifurcation in a driven laser system: experiment and theory. Phys Rev E Stat Nonlin Soft Matter Phys, 70(2 Pt 2), 026220. doi:10.1103/PhysRevE.70.026220