The geodynamo as a low-dimensional deterministic system at the edge of chaos

Ryan, D. A.; Sarson, Graeme R.

doi:10.1209/0295-5075/83/49001

Cited by 19 publications

(14 citation statements)

References 27 publications

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“…Several studies have shown how features of the Earth paleomagnetic records [8,9] or sunspots activity [10,11], can be described as the dynamics of a low dimensional system. In the VKS experiment, the low dimensional nature of the dynamics of the magnetic field has been emphasized in [12].…”

Section: Comparison With a Modelmentioning

confidence: 99%

Dynamo regimes and transitions in the VKS experiment

et al. 2010

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Abstract. The Von Kármán Sodium experiment yields a variety of dynamo regimes, when asymmetry is imparted to the flow by rotating impellers at different speed F1 and F2. We show that as the intensity of forcing, measured as F1 + F2, is increased, the transition to a self-sustained magnetic field is always observed via a supercritical bifurcation to a stationary state. For some values of the asymmetry parameter θ = (F1−F2)/(F1+F2), time dependent dynamo regimes develop. They are observed either when the forcing is increased for a given value of asymmetry, or when the amount of asymmetry is varied at sufficiently high forcing. Two qualitatively different transitions between oscillatory and stationary regimes are reported, involving or not a strong divergence of the period of oscillations. These transitions can be interpreted using a low dimensional model based on the interactions of two dynamo modes. PACS

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Section: Comparison With a Modelmentioning

confidence: 99%

Dynamo regimes and transitions in the VKS experiment

et al. 2010

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“…It has been further developed theoretically (Gao et al, 2009, 2012b) and applied to characterize EEG (Gao et al, 2011a, 2012c), HRV (Hu et al, 2009a, 2010), financial time series (Gao et al, 2011c), and Earth's geodynamo (Ryan and Sarson, 2008). Recently, SDLE is compared with a number of entropy measures (Gao et al, 2012c).…”

Section: Methodsmentioning

confidence: 99%

Multiscale analysis of heart rate variability in non-stationary environments

Gao

Gurbaxani²,

Hu³

et al. 2013

Front. Physiol.

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Heart rate variability (HRV) is highly non-stationary, even if no perturbing influences can be identified during the recording of the data. The non-stationarity becomes more profound when HRV data are measured in intrinsically non-stationary environments, such as social stress. In general, HRV data measured in such situations are more difficult to analyze than those measured in constant environments. In this paper, we analyze HRV data measured during a social stress test using two multiscale approaches, the adaptive fractal analysis (AFA) and scale-dependent Lyapunov exponent (SDLE), for the purpose of uncovering differences in HRV between chronic fatigue syndrome (CFS) patients and their matched-controls. CFS is a debilitating, heterogeneous illness with no known biomarker. HRV has shown some promise recently as a non-invasive measure of subtle physiological disturbances and trauma that are otherwise difficult to assess. If the HRV in persons with CFS are significantly different from their healthy controls, then certain cardiac irregularities may constitute good candidate biomarkers for CFS. Our multiscale analyses show that there are notable differences in HRV between CFS and their matched controls before a social stress test, but these differences seem to diminish during the test. These analyses illustrate that the two employed multiscale approaches could be useful for the analysis of HRV measured in various environments, both stationary and non-stationary.

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“…Hoping to characterize a complex time series on a broad range of scales simultaneously, recently, a new multiscale complexity measure, the scale-dependent Lyapunov exponent (SDLE), has been developed. SDLE was first introduced in (Gao et al, 2006c;Gao et al, 2007), and has been further developed in (Gao et al, 2009;Gao et al, 2012b) and applied to characterize EEG (Gao et al, 2011c), HRV (Hu et al, 2009a;Hu et al, 2010), financial time series (Gao et al, 2011a), and Earth's geodynamo (Ryan et al, 2008).…”

Section: Multiscale Analysis Of Geophysical Data By the Scale-dependementioning

confidence: 99%

Analyses of geographical observations in the Heihe River Basin: Perspectives from complexity theory

2019

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Since 2005, dozens of geographical observational stations have been established in the Heihe River Basin (HRB), and by now a large amount of meteorological, hydrological, and ecological observations as well as data pertaining to water resources, soil and vegetation have been collected. To adequately analyze these available data and data to be further collected in future, we present a perspective from complexity theory. The concrete materials covered include a presentation of adaptive multiscale filter, which can readily determine arbitrary trends, maximally reduce noise, and reliably perform fractal and multifractal analysis, and a presentation of scale-dependent Lyapunov exponent (SDLE), which can reliably distinguish deterministic chaos from random processes, determine the error doubling time for prediction, and obtain the defining parameters of the process examined. The adaptive filter is illustrated by applying it to obtain the global warming trend and the Atlantic multidecadal oscillation from sea surface temperature data, and by applying it to some variables collected at the HRB to determine diurnal cycle and fractal properties. The SDLE is illustrated to determine intermittent chaos from river flow data.

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The geodynamo as a low-dimensional deterministic system at the edge of chaos

Cited by 19 publications

References 27 publications

Dynamo regimes and transitions in the VKS experiment

Dynamo regimes and transitions in the VKS experiment

Multiscale analysis of heart rate variability in non-stationary environments

Analyses of geographical observations in the Heihe River Basin: Perspectives from complexity theory

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