Abstract

Forward-feed, hidden-layer, neural network (FFNN) algorithms, with nonlinear thresholding functions, trained on a chaotic time series, are shown to constitute a global approximation to the chaotic phase space attractor. As a function generator, a FFNN, trained on an arbitrary chaotic time series, forms a functional realization of that time series, i.e., the FFNN can “learn” the underlying rules/equations that generate chaotic dynamics. We present results from several model calculations, including that for the single-mode laser, the Duffing oscillator, and the Ikeda model to demonstrate characterization, with respect to the phase space attractors, self-generation for effective data window extension of stationary time series, and multistep prediction commensurate with the associated Lyapunov critical component. In addition, we apply our new method of analysis to the study of stimulated Brillouin scattering (SBS) of light from a cw-pumped optical fiber. We use our FFNN method to clearly demarcate purely deterministic from purely stochastic contributions in the SBS temporal evolution by using signal generation from the standard stochastic SBS equations. Results are analyzed for regions of the parameter space and conditions that include those of corresponding reported experiments.

© 1992 Optical Society of America