Analysis and prediction of aperiodic hydrodynamic oscillatory time series by feed-forward neural networks, fuzzy logic, and a local nonlinear predictor

Abstract

Forecasting of aperiodic time series is a compelling challenge for science. In this work, we analyze aperiodic spectrophotometric data, proportional to the concentrations of two forms of a thermoreversible photochromic spiro-oxazine, that are generated when a cuvette containing a solution of the spiro-oxazine undergoes photoreaction and convection due to localized ultraviolet illumination. We construct the phase space for the system using Takens' theorem and we calculate the Lyapunov exponents and the correlation dimensions to ascertain the chaotic character of the time series. Finally, we predict the time series using three distinct methods: a feed-forward neural network, fuzzy logic, and a local nonlinear predictor. We compare the performances of these three methods.