Prognosis of System Qualitative Behavior by Noisy Nonstationary Chaotic Time-Series

An approach to prognosis of behavior of an unknown dynamical system (DS) from weakly nonstationary chaotic time series (TS) containing significant measurement noise is proposed. The approach is based on construction of a global time-dependent parametrized model of discrete evolution operator capable of reproducing nonstationary dynamics of reconstructed DS. A universal model in the form of artificial neural network (ANN) with certain prior limitations is proposed. Probabilistic prognosis of the system behavior is performed using Monte-Carlo Markov Chain (MCMC) analysis of the posterior Bayesian distribution of the model parameters. The ability of the approach to provide prognosis for times greater than observation time interval is demonstrated. Some restrictions as well as possible advances of the proposed approach are discussed.