Correlation Dimension of the Strange Attractor for Geomagnetic Field Variations

2013 ◽  
pp. 103-107
Author(s):  
Yu. S. Tyupkin ◽  
A. Ya. Feldstein
Keyword(s):  
Strange Attractor ◽  
Geomagnetic Field ◽  
Correlation Dimension

scholarly journals Evidence for nonlinear and chaotic behaviour in pulsar spin-down rates

2012 ◽  
Vol 8 (S291) ◽  
pp. 495-495
Author(s):  
Andrew Seymour ◽  
Duncan Lorimer
Keyword(s):  
Time Series ◽  
Lyapunov Exponent ◽  
Nonlinear Equations ◽  
Strange Attractor ◽  
Correlation Dimension ◽  
Chaotic Dynamics ◽  
Structural Information ◽  
Chaotic Behaviour ◽  
Present Evidence

AbstractWe present evidence for chaotic dynamics in pulsar spin-down rates originally measured by Lyne et al. (2010). Using techniques that allow us to re-sample the original measurements without losing structural information, we have searched for evidence for a strange attractor in the time series of frequency derivative for each pulsar. Our measurements of correlation dimension and Lyapunov exponent show, particularly in the case of PSR B1828-11, that the underlying behavior appears to be driven by a strange attractor with approximately three governing nonlinear equations.

Numerical Research on Self-Sustained Oscillation and Chaos of Natural Convection in Horizontal Fluids Layer

2013 ◽  
Vol 448-453 ◽  
pp. 3234-3239
Author(s):  
Nai Yan Zhan ◽  
Bo Li ◽  
Y. Xiao
Keyword(s):  
Numerical Simulation ◽  
Natural Convection ◽  
Strange Attractor ◽  
Stability Problem ◽  
Correlation Dimension ◽  
Simple Algorithm ◽  
Sustained Oscillation ◽  
Quick Scheme ◽  
Numerical Research ◽  
Chaos Attractor

Numerical simulation was conducted to study self-sustained oscillation and chaos of natural convection in horizontal fluids layer heated from below. The numerical simulation was conducted using SIMPLE algorithm with a QUICK scheme. Discrete time series was analyzed to study stability problem. Correlation dimension was calculated, their frequency characteristics were analyzed and chaos attractor was extracted. The results showed that oscillation appeared when Ra was over 2×104 and chaos appeared when Ra was over 5×106. When parameter was varied, chaos appeared. Strange attractor was used to describe chaos system. Fractal dimension of strange attractor was 1.19. Saturated embedding dimension of phase space reconstruction was 5. The time delay was selected for 5.

Models of the geomagnetic field and characteristics of magnetic storms

2006 ◽  
Vol 12 (1) ◽  
pp. 64-69
Author(s):  
O.I. Maksimenko ◽  
◽  
L.N. Yaremenko ◽  
O.Ya. Shenderovskaya ◽  
G.V. Melnyk ◽  
...  
Keyword(s):  
Geomagnetic Field ◽  
Magnetic Storms

MicroVolt Variations of The Human Brain (Quantitative Electroencephalography) Display Differential Torque Effects During West-East versus North-South Orientation in the Geomagnetic Field

2016 ◽  
Vol 12 (2) ◽  
pp. 4255-4259
Author(s):  
Michael A Persinger ◽  
David A Vares ◽  
Paula L Corradini
Keyword(s):  
Human Brain ◽  
Geomagnetic Field ◽  
Neuronal Cell ◽  
Single Subject ◽  
Additional Energy ◽  
Actual Measurement ◽  
Neuronal Processes ◽  
Basic Physics ◽  
Order Of Magnitude ◽  
The Moment

                The human brain was assumed to be an elliptical electric dipole. Repeated quantitative electroencephalographic measurements over several weeks were completed for a single subject who sat in either a magnetic eastward or magnetic southward direction. The predicted potential difference equivalence for the torque while facing perpendicular (west-to-east) to the northward component of the geomagnetic field (relative to facing south) was 4 μV. The actual measurement was 10 μV. The oscillation frequency around the central equilibrium based upon the summed units of neuronal processes within the cerebral cortices for the moment of inertia was 1 to 2 ms which are the boundaries for the action potential of axons and the latencies for diffusion of neurotransmitters. The calculated additional energy available to each neuron within the human cerebrum during the torque condition was ~10-20 J which is the same order of magnitude as the energy associated with action potentials, resting membrane potentials, and ligand-receptor binding. It is also the basic energy at the level of the neuronal cell membrane that originates from gravitational forces upon a single cell and the local expression of the uniaxial magnetic anisotropic constant for ferritin which occurs in the brain. These results indicate that the more complex electrophysiological functions that are strongly correlated with cognitive and related human properties can be described by basic physics and may respond to specific geomagnetic spatial orientation.

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