Extracting quantitative measures from finite length nonlinear timeseries- complex systems approaches

Details Extracting quantitative measures from finite length nonlinear timeseries- complex systems approaches Extracting quantitative measures from finite length nonlinear timeseries- complex systems approaches

Dec 2006

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=2006agufmsm21c0277w&link_type=abstract

American Geophysical Union, Fall Meeting 2006, abstract #SM21C-0277

Mathematics

Probability

4430 Complex Systems, 4465 Phase Transitions, 4468 Probability Distributions, Heavy And Fat-Tailed (3265), 4475 Scaling: Spatial And Temporal (1872, 3270, 4277), 4490 Turbulence (3379, 4568, 7863)

Scientific paper

We consider two complex systems approaches to obtaining quantitative measures from `real world' timeseries, such as in situ solar wind observations and geomagnetic indices, where information about the process in not known a priori. The first is statistical- we discuss the problem of obtaining the scaling exponents from the PDF of fluctuations (differenced variables) via PDF collapse and structure functions. If the probability density is heavy tailed, outliers strongly influence the scaling behaviour of the moments. From an operational point of view, we wish to recover the scaling exponents of the underlying process by excluding a minimal population of these outliers. We test these ideas on a synthetically generated symmetric alpha-stable Lèvy process and show that the Lèvy exponent is recovered in up to the 6th order moment after ~0.1-0.5% of the data are excluded. The scaling properties of the excluded outliers can then be tested to provide additional information about the system. We highlight application of this technique to in- situ spacecraft observation of the turbulent solar wind and to geomagnetic indices. The second of these is dynamical- we explore the use of Mutual Information (MI) as a method to determine order- disorder transitions and test this idea on the Viscek `boid' model for flocking. We compare MI with the full system susceptibility we demonstrate that MI can pinpoint the phase transition with reasonable accuracy. We also consider the MI as a tool for detecting nonlinear correlation between different systems with application to `space weather', that is, solar wind triggering of geomagnetic activity on the earth.

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