Fisher-Shannon Investigation of the Effect of Nonlinearity of Discrete Langevin Model on Behavior of Extremes in Generated Time Series.

Diverse forms of nonlinearity within stochastic equations give rise to varying dynamics in processes, which may influence the behavior of extreme values. This study focuses on two nonlinear models of the discrete Langevin equation: one with a fixed diffusion function (M1) and the other with a fixed marginal distribution (M2), both characterized by a nonlinearity parameter. Extremes are defined according to the run theory with thresholds based on percentiles.

Effect of nonlinearity and persistence on multiscale irreversibility, non-stationarity, and complexity of time series-Case of data generated by the modified Langevin model.

Stochastic models of a time series can take the form of a nonlinear equation and have a built-in memory mechanism. Generated time series can be characterized by measures of certain features, e.g.

Discrete Langevin-type equation for p-order persistent time series and procedure of its reconstruction.

The stochastic discrete Langevin-type equation, which can describe p-order persistent processes, was introduced. The procedure of reconstruction of the equation from time series was proposed and tested on synthetic data. The approach was applied to hydrological data leading to the stochastic model of the phenomenon.

Clustering of extreme events in time series generated by the fractional Ornstein-Uhlenbeck equation.

We analyze the time clustering phenomenon in sequences of extremes of time series generated by the fractional Ornstein-Uhlenbeck (fO-U) equation as the source of long-term correlation. We used the percentile-based definition of extremes based on the crossing theory or run theory, where a run is a sequence of L contiguous values above a given percentile. Thus, a sequence of extremes becomes a point process in time, being the time of occurrence of the extreme the starting time of the run.

Time series analysis in earthquake complex networks.

We introduce a new method of characterizing the seismic complex systems using a procedure of transformation from complex networks into time series. The undirected complex network is constructed from seismic hypocenters data. Network nodes are marked by their connectivity.

Relation between HVG-irreversibility and persistence in the modified Langevin equation.

In this study, we investigate the relationship between persistence/antipersistence and time-irreversibility by using the Kullback-Leibler Divergence (KLD) in the directed Horizontal Visibility Graph applied to a new modified Langevin equation with persistence parameter d. A non-trivial relationship KLD(d) was found, characterized by a non-symmetric shape, which suggests that time-irreversibility increases with the degree of persistence or antipersistence. The analysis is applied to the population growth model, where the level of irreversibility may represent important features of the population dynamics, like its stability and ecosystem health.

Bi-SOC-states in one-dimensional random cellular automaton.

Two statistically stationary states with power-law scaling of avalanches are found in a simple 1 D cellular automaton. Features of the fixed points, the spiral saddle and the saddle with index 1, are investigated. The migration of states of the automaton between these two self-organized criticality states is demonstrated during evolution of the system in computer simulations.

Detrended fluctuation analysis of the Ornstein-Uhlenbeck process: Stationarity versus nonstationarity.

The stationary/nonstationary regimes of time series generated by the discrete version of the Ornstein-Uhlenbeck equation are studied by using the detrended fluctuation analysis. Our findings point out to the prevalence of the drift parameter in determining the crossover time between the nonstationary and stationary regimes. The fluctuation functions coincide in the nonstationary regime for a constant diffusion parameter, and in the stationary regime for a constant ratio between the drift and diffusion stochastic forces.

Reconstruction of the modified discrete Langevin equation from persistent time series.

The discrete Langevin-type equation, which can describe persistent processes, was introduced. The procedure of reconstruction of the equation from time series was proposed and tested on synthetic data, with short and long-tail distributions, generated by different Langevin equations. Corrections due to the finite sampling rates were derived.

Multifractal analysis of visibility graph-based Ito-related connectivity time series.

In this study, we investigate multifractal properties of connectivity time series resulting from the visibility graph applied to normally distributed time series generated by the Ito equations with multiplicative power-law noise. We show that multifractality of the connectivity time series (i.e.

Multifractal analysis of time series generated by discrete Ito equations.

In this study, we show that discrete Ito equations with short-tail Gaussian marginal distribution function generate multifractal time series. The multifractality is due to the nonlinear correlations, which are hidden in Markov processes and are generated by the interrelation between the drift and the multiplicative stochastic forces in the Ito equation. A link between the range of the generalized Hurst exponents and the mean of the squares of all averaged net forces is suggested.