ABSTRACT
The characterization of nonlinear and chaotic systems has become increasingly important in many areas of science and engineering (Campbell and Rose 1983). Features such as broadband power spectra and a lack of long-term predictability often make chaotic phenomena difficult to distinguish from purely random processes. In characterizing data, the most basic question to ask is whether or not the data is deterministic, and if so, what dimensionality? To this end, we show that neural networks can be used to detect determinism and to estimate dimensionality. Furthermore, we show that neural networks are capable of detecting multiple processes with different dimensionality in the same data set. Model-generated chaotic time series from the Mackey-Glass systems (Raisband 1990) are used to measure performance and robustness. The procedure is applied to the analysis of experimental results of spontaneously generated Brillouin signals from intense laser-field-excited single-model fibers (Harrison et al 1990).
