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

Abstract

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.

Principal nonlinear dynamical modes of climate variability

“…Thus, it is reasonable to define this PDF as a product of Gaussian functions of each with variance , where 〈.〉 denotes average over time. The same restrictions of parameters were used, for instance, in3435 regarding to external layer coefficients of artificial neural networks used for fitting an evolution operator.…”

Amphetamine enhances endurance by increasing heat dissipation

“…where k = saline or Amph, and N = 13 and 15 for saline and Amph, respectively. The likelihood (equation 3) was sampled using Markov Chain Monte Carlo approach by Metropolis-Hastings algorithm (Mukhin et al 2006;Loskutov et al 2008;Molkov et al 2011Molkov et al , 2012Robert et al).…”

Estimation of Characteristics of Delayed Coupling Between Stochastic Oscillators from the Observed Phase Dynamics

“…Figure 6d shows the estimate of the autocorrelation function of noise in the phase dynamics of the NAO, and the time of its decay in absolute value to 0.2 is 176 months, which significantly exceeds τ = 32 months, so that Eq. (6) proposed in this work was used for estimating the delay time. The corresponding point estimateΔ corr 2→1 of the delay time is equal to 36 months, while the confidence interval amounts to 25-47 months.…”

“…Such problems can involve prediction of the qualitative variations in the dynamics [5,6] and estimation of the characteristics of interaction (coupling) among the complex-system elements [7][8][9]. Along with the deterministic nonlinear models [1][2][3], much attention is given to the development of the stochastic model equations [3][4][5][6][10][11][12][13] also when estimating the directional-coupling characteristics by empirical simulation of the phase dynamics [8,14].…”