Nonlinear time series analysis of the human electrocardiogram

Perc, Matjaž

doi:10.1088/0143-0807/26/5/008

Cited by 97 publications

(59 citation statements)

References 56 publications

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“…These parameters are estimated via the False Nearest Neighbor (FNN) algorithm (i.e., embedding dimension m) and as the first minimum of the Mutual Information (MI) method (i.e., time delay τ ), using the programs described in Kodba et al (2005) and Perc (2005aPerc ( , 2005bPerc ( , 2006. These .exe programs (fnn, mutual and others) are available from the website.…”

Section: Takens Reconstructionmentioning

confidence: 99%

“…For a detailed description of these algorithms, see Kodba et al (2005), Perc (2005aPerc ( , 2005bPerc ( , 2006 and Hegger et al (1999) for another common implementation. The parameters m and τ are both required for the mLE calculation.…”

Section: For Nearby Points S(i) S(t) Such That S(i) − S(t) <mentioning

confidence: 99%

“…The mLE, denoted λ in general, was calculated using two distinct algorithms: the Wolf et al (1985) and Kantz (1994) methods, incorporated in the programs lyapmax and lyapmaxk (Kodba et al 2005;Perc 2005aPerc , 2005bPerc , 2006, and lyap_k from the TISEAN package. Herein the results of those investigations are presented.…”

Section: Maximal Lyapunov Exponentmentioning

confidence: 99%

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Nonlinear time-series analysis of Hyperion’s lightcurves

Tarnopolski

2015

Astrophys Space Sci

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Hyperion is a satellite of Saturn that was predicted to remain in a chaotic rotational state. This was confirmed to some extent by Voyager 2 and Cassini series of images and some ground-based photometric observations. The aim of this article is to explore conditions for potential observations to meet in order to estimate a maximal Lyapunov Exponent (mLE), which being positive is an indicator of chaos and allows to characterise it quantitatively. Lightcurves existing in literature as well as numerical simulations are examined using standard tools of theory of chaos. It is found that existing datasets are too short and undersampled to detect a positive mLE, although its presence is not rejected. Analysis of simulated lightcurves leads to an assertion that observations from one site should be performed over a year-long period to detect a positive mLE, if present, in a reliable way. Another approach would be to use 2-3 telescopes spread over the world to have observations distributed more uniformly. This may be achieved without disrupting other observational projects being conducted. The necessity of time-series to be stationary is highly stressed.

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Section: Takens Reconstructionmentioning

confidence: 99%

Section: For Nearby Points S(i) S(t) Such That S(i) − S(t) <mentioning

confidence: 99%

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Nonlinear time-series analysis of Hyperion’s lightcurves

Tarnopolski

2015

Astrophys Space Sci

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“…Nonlinear time series analysis is a powerful theory, which could be used to extract the characteristic quantities of a particular system solely by analyzing the time course of one of its variables. Thus, the theory of nonlinear time series analysis offers tools that bridge the gap between the experimentally observed irregular behavior and the deterministic chaos theory 32 . Recurrence is a fundamental characteristic of many dynamical systems introduced by Poincaré in 1890.…”

Section: Introductionmentioning

confidence: 99%

Recurrence Quantity Analysis of the Instantaneous Pressure Fluctuation Signals in the Novel Tank with Multi-Horizontal Submerged Jets

Meng

Song

et al. 2016

Chem.Biochem.Eng.Q.

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The circulating jet tank (CJT) has been an alternative piece of equipment for mixing instead of the bottom-stirring tank, which is widely used in industrial applications. The recurrence plots (RPs) and recurrence quantification analysis (RQA) of pressure fluctuation signals (PFS) in the novel CJT were employed to reflect the chaotic extent of jet mixing. The recurrence rate, determinism and averaged diagonal line length of PFS were evaluated at different Reynolds numbers, radial positions and axial positions. The profiles of recurrence rate, determinism and averaged diagonal line length had similar tendency with the increasing Re, which showed that the determinism of PFS increased and the randomness of the chaotic system became small. With the increase in z/H, the recurrence characteristics of PFS at θ m = π/6 gradually increased, which were smaller than that of other θ m . The results of this study provide a deep understanding of the hydrodynamics in the CJT, and thus lay a foundation for further design optimization.

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“…Let us now look back at the actual scenario. Deterministic chaos was observed in many different real-life phenomena that include some Hindustani classical music, some bio-medical signals like ECG [35] and EMG signals, etc. Recently, deterministic chaos was observed in systems as diverse as insects [36][37], reptiles [38] and by laser droplet generation [39].…”

Section: Introductionmentioning

confidence: 99%

New types of nonlinear auto-correlations of bivariate data and their applications

Palit¹,

Mukherjee²,

Bhattacharya

2012

Applied Mathematics and Computation

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Abstract. The paper introduces new types of nonlinear correlations between bivariate data sets and derives nonlinear auto-correlations on the same data set. These auto-correlations are of different types to match signals with different types of nonlinearities. Examples are cited in all cases to make the definitions meaningful. Next correlogram diagrams are drawn separately in all cases; from these diagrams proper time lags/delays are determined. These give rise to independent coordinates of the attractors. Finally three dimensional attractors are reconstructed in each case separately with the help of these independent coordinates. Moreover for the purpose of making proper distinction between the signals, the attractors so reconstructed are quantified by a new technique called 'ellipsoid fit'.

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Nonlinear time series analysis of the human electrocardiogram

Cited by 97 publications

References 56 publications

Nonlinear time-series analysis of Hyperion’s lightcurves

Nonlinear time-series analysis of Hyperion’s lightcurves

Recurrence Quantity Analysis of the Instantaneous Pressure Fluctuation Signals in the Novel Tank with Multi-Horizontal Submerged Jets

New types of nonlinear auto-correlations of bivariate data and their applications

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