Correlation Integral Analysis Research Articles

Nonlinear dynamics of laser systems with elements of a chaos: Advanced computational code

A general, uniform chaos-geometric computational approach to analysis, modelling and prediction of the non-linear dynamics of quantum and laser systems (laser and quantum generators system etc) with elements of the deterministic chaos is briefly presented. The approach is based on using the advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov’s exponents analysis, and surrogate data method, prediction models etc There are firstly presented the numerical data on the topological and dynamical invariants (in particular, the correlation, embedding, Kaplan-York dimensions, the Lyapunov’s exponents, Kolmogorov’s entropy and other parameters) for laser system (the semiconductor GaAs/GaAlAs laser with a retarded feedback) dynamics in a chaotic and hyperchaotic regimes.

NONLINEAR CHAOTIC DYNAMICS OF ATOMIC AND MOLECULAR SYSTEMS IN AN ELECTROMAGNETIC FIELD

It has been numerically studied a chaotic dynamics of diatomic molecules (on example of the GeO molecule in an infrared field) and some laser systems. An advanced generalized techniques such as the wavelet analysis, multi-fractal formalism, mutual information approach, correlation integral analysis, false nearest neighbour algorithm, the Lyapunov exponent’s (LE) analysis, and surrogate data method, prediction models etc is used. It has been shown that systems exhibit a nonlinear behaviour with elements of a low-or high-dimensional chaos. There are firstly presented the numerical data on topological and dynamical invariants of chaotic systems, in particular, the correlation, embedding, Kaplan-York dimensions, LE, Kolmogorov’s entropy etc for GeO molecule in an electromagnetic infrared field in the chaotic regime.

Новый хаос-геометрический и информационный подход к анализу режима хаотической генерации в одно-модовой лазерной системе с поглощающей ячейкой

Here we present the results of application of a new chaos-geometric approach and some information technology algorithms to analysis of chaotic generation regime in a single-mode laser system with absorbing cell. Earlier developed chaos-geometric approach to modelling and analysis of nonlinear processes dynamics of the complex systems combines together application of the advanced mutual information approach, correlation integral analysis, Lyapunov exponent's analysis etc.

Хаос-геометрический подход к анализу динамики хаотического аттрактора для одно-кольцевого волоконного лазера

Earlier we have developed new chaos-geometric approach to modelling and analysis of nonlinear processes dynamics of the complex systems. It combines together application of the advanced mutual information approach, correlation integral analysis, Lyapunov exponent's analysis etc. Here we present the results of its application to studying low-and high-D attractor dynamics of the one-ring fibre laser

Хаос-геометрический подход к анализу хаотической динамики

Within chaos-geometric approach it has been carried out modelling and analysis of nonlinear processes dynamics in quantum-generator system (time series of laser intensities). The approach combines together application of the advanced mutual information approach, correlation integral analysis, Lyapunov exponent's analysis etc.

Nonlinear Analysis and Prediction of Coarse Particulate Matter Concentration in Ambient Air

This study attempts to characterize and predict coarse particulate matter (PM10) concentration in ambient air using the concepts of nonlinear dynamical theory. PM10 data observed daily from 1999 to 2002 at a site in Mumbai, India, was used to study the applicability of the chaos theory. First, the autocorrelation function and Fourier power spectrum were used to analyze the behavior of the time–series. The dynamics of the time–series was additionally studied through correlation integral analysis and phase space reconstruction. The nonlinear predictions were then obtained using local polynomial approximation based on the reconstructed phase space. The results were then compared with the autoregressive model. The results of nonlinear analysis indicated the presence of chaotic character in the PM10 time–series. It was also observed that the nonlinear local approximation outperforms the autoregressive model, because the observed relative error of prediction for the autoregressive model was greater than the local approximation model. The invariant measures of nonlinear dynamics computed for the predicted time–series using the two models also supported the same findings.

Effect of Regular and Irregular Missing Data on the Correlation Integral Analysis of Real-Time Series

Missing data which inevitably occurs in observed time series may lead to an erroneous result based on the correlation integral analysis. Effects of data, missing at regular and irregular times, on the analyzed result are estimated. A model estimation is obtained for the Lorenz time series. The effects of the missing data in economic and astronomical time series are estimated using the correlation integral analysis. A convenient method of choosing a time lag is proposed to minimize the effect of regularly missing data.

MULTI-SCALE CHARACTERISTICS OF CHAOS BEHAVIOR IN GAS-LIQUID BUBBLE COLUMNS

The multi-value phenomenon of correlation dimension appearing in chaos analysis of time series of pressure fluctuation obtained from gas-liquid bubble columns was studied. Its relationship with multi-scale flow behavior and possible application in the identification of flow regime and regime transition in bubble columns were investigated. The results indicated that the multi-value phenomenon of correlation dimension results from the multi-scale behavior existing in the heterogeneous churn flow regime in bubble columns. When a bubble column is in the homogeneous flow regime, only one correlation dimension is found at a specified superficial gas velocity, indicating that single-scale behavior is dominant in the system. When a bubble column is in the heterogeneous churn flow regime, multi- (generally three) correlation dimensions can be obtained, showing the appearance of multi-scale behavior. Therefore, the formulation of an effective flow model depends on an appropriate multi-scale analysis for bubble columns. Flow regime and regime transition can be characterized by the structure and structure variation of the plot of the correlation integral versus radius of the hyper-sphere. On the basis of the above analysis, a complementary potential methodology called correlation integral analysis for the identification of flow regime and regime transition in gas-liquid bubble columns is recommended.

Characterization and prediction of runoff dynamics: a nonlinear dynamical view

An attempt is made in this study to characterize and predict runoff dynamics, using ideas gained from nonlinear dynamical theory. Daily runoff data observed over a period of 19 years (January 1, 1975–December 31, 1993) at the Lindenborg catchment in Denmark is studied using a variety of techniques. First, the autocorrelation function and the Fourier power spectrum are used as indicators to obtain some preliminary information regarding the runoff behavior. A comprehensive characterization is done next through the correlation integral analysis, the false nearest neighbor algorithm, and the nonlinear prediction method, all of which use the concept of phase-space reconstruction, i.e., reconstruction of the single-dimensional (or variable) runoff series in a multi-dimensional phase-space to represent its dynamics. The average mutual information method is used to estimate the delay time for the phase-space reconstruction. The exponential decay in the autocorrelation function plot and the sharp spectral lines in the Fourier power spectrum seem to provide some preliminary indication regarding the possible presence of chaos in the runoff dynamics. The (low) correlation dimension (of about 3.76) obtained from the correlation integral analysis, the (low) global dimension (of 4 or 5) obtained from the false nearest neighbor algorithm, and the (low) optimal embedding dimension (of 3) from the nonlinear prediction method are in close agreement with each other, providing convincing evidence regarding the presence of low-dimensional chaotic behavior in the runoff dynamics. The near-accurate predictions achieved for the runoff series (correlation coefficient of about 0.99 and coefficient of efficiency of about 0.98) indicate the appropriateness of the chaotic dynamical approach for characterizing and predicting the runoff dynamics at the Lindenborg catchment.

Does the river run wild? Assessing chaos in hydrological systems

The standing debate over whether hydrological systems are deterministic or stochastic has been taken to a new level by controversial applications of chaos mathematics. This paper reviews the procedure, constraints, and past usage of a popular chaos time series analysis method, correlation integral analysis, in hydrology and adds a new analysis of daily streamflow from a pristine watershed. Significant problems with the use of correlation integral analysis (CIA) were found to include a continued reliance on the original algorithm even though it was corrected subsequently and failure to consider the physics underlying mathematical results. The new analysis of daily streamflow reported here found no attractor with D⩽5. Phase randomization of the Fourier Transform of streamflow was used to provide a better stochastic surrogate than an Autoregressive Moving Average (ARMA) model or gaussian noise for distinguishing between chaotic and stochastic dynamics.

Luminosity variations of 3C 345: Is there any evidence of low-dimensional chaos ?

view Abstract Citations (11) References (40) Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Luminosity Variations of 3C 345: Is There Any Evidence of Low-dimensional Chaos? Provenzale, A. ; Vio, R. ; Cristiani, S. Abstract We analyze the light curve of the optically violent variable quasar 3C 345, with the goal of determining the possible presence of low- dimensional chaos in the system dynamics. The results of the phase-space reconstruction and of the correlation integral analysis provide a convergent, noninteger estimate of the correlation dimension, naively suggesting the presence of deterministic chaos. However, we show that this result is generated by the long memory and by the power-law shape of the power spectrum of the signal, with no relationship to any underlying chaotic behavior. In fact, the light curve of 3C 345 is consistent with the output of a nonlinear stochastic process, and it is characterized by a well-defined intermittent nature. Publication: The Astrophysical Journal Pub Date: June 1994 DOI: 10.1086/174267 Bibcode: 1994ApJ...428..591P Keywords: Light Curve; Luminous Intensity; Nonlinearity; Quasars; Stochastic Processes; Variations; Correlation; Embedding; Integrals; Numerical Analysis; Procedures; Time Dependence; Astrophysics; METHODS: NUMERICAL; GALAXIES: QUASARS: INDIVIDUAL ALPHANUMERIC: 3C 345 full text sources ADS | data products SIMBAD (1) NED (1)