Prognosis of qualitative system behavior by noisy, nonstationary, chaotic time series

An approach to prognosis of qualitative 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 oper...

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Veröffentlicht in:Physical review. E, Statistical, nonlinear, and soft matter physics Statistical, nonlinear, and soft matter physics, 2011-09, Vol.84 (3 Pt 2), p.036215-036215, Article 036215
Hauptverfasser: Molkov, Y I, Mukhin, D N, Loskutov, E M, Timushev, R I, Feigin, A M
Format: Artikel
Sprache:eng
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Zusammenfassung:An approach to prognosis of qualitative 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 (EO) capable of reproducing nonstationary dynamics of a reconstructed DS. A universal model in the form of artificial neural network (ANN) with certain prior limitations is used for the approximation of the EO in the reconstructed phase space. 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 classification of qualitatively different regimes is supposed to be dictated by the application, i.e., it is assumed that some classifier function is predefined that maps a point of a model parameter space to a finite set of different behavior types. The ability of the approach to provide prognosis for times comparable to the observation time interval is demonstrated. Some restrictions as well as possible advances of the proposed approach are discussed.
ISSN:1539-3755
1550-2376
DOI:10.1103/PhysRevE.84.036215