Soil temperature can fluctuate dynamically, suggesting a possible chaotic behavior in such time series, as this can have a significant bearing on hydrological models, solar energy and other agricultural applications. Hence, this paper reports an investigation into the detection of a possible existence of chaotic behavior in the monthly soil temperature time series at five depths (5, 10, 20, 50 ...

Several methods have been suggested to predict the onset of epileptic seizures from EEG data. We evaluated the performance of three predictions methods: the “dynamical similarity index”, the “effective correlation dimension” and an extended, prospective version of the “accumulated energy”. These prediction methods were applied on a large pool of intracranial EEG data from 21 patients. Altogethe...

Cluster-Weighted Modeling, a mixture density estimator around local models, is presented as a framework for the analysis, prediction and characterization of non-linear time series. First architecture, model estimation and characterization formalisms are introduced. The characterization tools include estimator uncertainty, predictor uncertainty and the correlation dimension of the data set. In t...

15 We analyse the tracks of clock-shifted pigeons from six releases to determine how pigeons cope with the conflict between their sun compass and the other navigational cues. Time-lag embedding is used to calculate the short-term correlation dimension, a parameter that reflects the complexity of the navigational system and with it, the number of factors involved. In the beginning, while pigeons...

The correlation dimension was calculated for a collection of 6080 strange attractors obtained numerically from low-degree polynomial, low-dimensional maps and flows. It was found that the average correlation dimension scales approximately as the square root of the dimension of the system with a surprisingly small variation. This result provides an estimate of the number of dynamical variables r...

The nonlinear dynamics of Chua’s circuit and its applications to communications is studied. Chaos is realized, and is investigated by calculating the Lyapunov exponent for the system. A three dimensional phase portrait for the characteristic double scroll is reconstructed from the two dimensional image, from which the correlation dimension is calculated. This experiment was done by designing Ch...

In the analysis of chaotic time series, a standard technique is to reconstruct an image of the original dynamical system using delay coordinates. If the original dynamical system has an attractor, then the correlation dimension D2 of its image in the reconstruction can be estimated using the Grassberger–Procaccia algorithm. The quality of the reconstruction can be probed by measuring the length...

Due to the close relationship between the correlation integral and the fractal dimension, it is natural to presume that the correlation integral is also capable of characterizing network traffic. In this paper, we use captured traffic traces to illustrate that one can indeed describe the dynamics of the Internet traffic with a template of correlation integrals. Furthermore, this template can be...

| The technique of surrogate data provides has been used to test for membership of particular classes of linear systems. Existing algorithms provide non-parametric methods to generate surrogates similar to the data and consistent with a given hypothesis. These non-parametric methods allow a wide range of test statistics to be utilized. We suggest an obvious extension of this to classes of nonli...

A technique for obtaining chaotic response from a stable first order conventional digital phase locked loop (DPLL) driven by another stable first order conventional DPLL has been reported in this paper. The dynamics of the driven system has been characterized using the dynamical measures of Lyapunov exponent and Correlation dimension. It is found that the resultant chaos is low dimensional, whi...