The low dimensionality of magnetospheric activity indicated by previous phase space reconstructions using the AE and AL data suffer from the limitations of these t chniques. In this paper the singular spectrum analysis is used to study the global magnetospheric dynamics using the AE data and it yields a correlation dimension m2.5, thus confirming the low dimensionality published earlier. Furthe...

The paper relates to possible connection between spectrum power-law decay and correlation dimension estimation for electroencephalogram (EEG). EEG signals recorded during relaxed wakefulness were analysed. Power-law decay of about 2.28 prevailing over the exponential falling off was established when exponent from the whole EEG spectrum was taken. The correlation dimension was also estimated. Th...

This paper investigates chaos in a Nigerian mutual fund, Asset and Resource Management Company Limited (ARM) for a period of eleven years. The existence of chaotic signals in the data was identified by the reconstruction of the phase space of the daily closing price of the fund and the delay time was quantified using mutual information function and the embedding dimension by the false nearest n...

Various phonemes are considered in terms of nonlinear dynamics. Phase portraits of the signals in the embedded space, correlation dimension estimate and the largest Lyapunov exponent are analyzed. It is shown that the speech signals have comparatively small dimension and the positive largest Lyapunov exponent

Statistical measures of determinism for spikes train are described and analyzed. The analysis is focused on two dynamical invariants: nonlinear forecastability and correlation dimension. Two simple, generic, biologically motivated methods for generating spikes from the system are surveyed: an integrate-and-fire model (IF) and a threshold-crossing method (TC). The effect on the statistical measu...

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We propose a new measure to characterize the dimension of complex networks based on the ergodic theory of dynamical systems. This measure is derived from the correlation sum of a trajectory generated by a random walker navigating the network, and extends the classical Grassberger-Procaccia algorithm to the context of complex networks. The method is validated with reliable results for both synth...

We examine the question whether the dimension D of a set or probability measure is the same as the dimension of its image under a typical smooth function, if the range space is at least D-dimensional. If is a Borel probability measure of bounded support in Rn with correlation dimension D, and if m D, then under almost every continuously differentiable function (“almost every” in the sense of pr...

This paper compares the correlation dimension (D2) and Higuchi fractal dimension (HFD) approaches in estimating BIS index based on of electroencephalogram (EEG). The single-channel EEG data was captured in both ICU and operating room and different anesthetic drugs, including propofol and isoflurane were used. For better analysis, application of adaptive segmentation on EEG signal for estimating...

We address the problem of distinguishing regular, chaotic, and random behavior using an electronic circuit modeling of a ball bouncing on an oscillating table. We calculate the correlation dimension of the system from time series data taken from the circuit, and show that this system seems amenable to correlation dimension analysis. In particular we find dimensions of 1.07 for regular data and ...