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We propose a new approach to reconstructing complex, spatially distributed systems on the basis of the time series generated by such systems. It allows one to combine two basic steps of such a reconstruction, namely, the choice of a set of phase variables of the system using the observed time series and the development of the evolution operator acting in the chosen phase space with the help of an artificial neural network with special topology. This network, first, maps the initial high-dimensional data onto the lower-dimension space and, second, specifies the evolution operator in this space. The efficiency of this approach is demonstrated by an example of reconstructing the Lorenz system representing a high-dimensional model of atmospheric dynamics.

We have found a set of correlation effects, which are due to the inherent dynamics of the spectral density of polarization of an active medium with strong inhomogeneous broadening of the working transition line and occur if the rate of incoherent relaxation of optical dipole oscillations of the active centers is lower than the rate of optical-field attenuation in the laser cavity. Our analysis is based on the numerical studies of the stationary superradiant laser generation during continuous pumping with self-locking of some of the quasistationary modes. For the purposes of studying the detected effects, the methods of comparative analysis of the dynamic spectra of polarization and the field have been developed. In these methods, the time-frequency and space-time empirical modes of the spectra are used, which are determined by orthogonal eigenfunctions of special correlation matrices. The interconnection of the superradiance phenomena and mode self-locking in the considered class of lasers with low-Q cavities is discussed.

A new data-driven model for analysis and prediction of spatially distributed time series is proposed. The model is based on a linear dynamical mode (LDM) decomposition of the observed data which is derived from a recently developed nonlinear dimensionality reduction approach. The key point of this approach is its ability to take into account simple dynamical properties of the observed system by means of revealing the system’s dominant time scales. The LDMs are used as new variables for empirical construction of a nonlinear stochastic evolution operator. The method is applied to the sea surface temperature anomaly field in the tropical belt where the El Nino Southern Oscillation (ENSO) is the main mode of variability. The advantage of LDMs versus traditionally used empirical orthogonal function decomposition is demonstrated for this data. Specifically, it is shown that the new model has a competitive ENSO forecast skill in comparison with the other existing ENSO models.

A nonlinear decomposition method is applied to the analysis of global sea surface temperature (SST) time series in different epochs related to the Pacific Decadal Oscillation (PDO) since the end of 19th century to present time. This method allows one to extract an optimal (small) number of global nonlinear teleconnection patterns associated with distinct dominant time scales from the original high-dimensional spatially extended data set. In particular, it enables us to reveal ENSO teleconnection patterns corresponding to different PDO cycles during the last 145 years, to uncover four climate shifts connected with PDO phase changes and to reconstruct the corresponding global PDO patterns. We find that SST teleconnections between the ENSO region, extra-tropical Pacific regions and the Indian ocean became fundamentally nonlinear since the second half of 20th century.

An approach to the long-term prognosis of qualitative behavior of a dynamic system (DS) is proposed, which is based on the nonlinear-dynamical analysis of a weakly nonstationary chaotic time series (TS). A method for constructing prognostic models using the observed evolution of a single dynamic variable is described, which employs the proposed approach for prediction of bifurcations of low-dimensional DSs. The method is applied to analyze the TS generated by the Roessler system and the system of equations modeling photochemical processes in the mesosphere. The analysis is performed for a TS calculated in the case of a slow variation in the control parameter of the system. The duration of the “observed” TS is limited such that the system demonstrates only one, chaotic, type of behavior without any bifurcations during the observed TS. The proposed algorithm allows us to predict correctly the bifurcation sequences for both systems at times much longer than the duration of the observed TS, to point out the expected instants of specific bifurcation transitions and accuracy of determining these instants, as well as to calculate the probabilities to observe the predicted regimes of the system's behavior at the time of interest.