Abstract
Correlation-dimension analysis is often used to quantify the dynamics of the obscure attractor from the measured time series. Specifically, the method of sliding-window correlation-dimension is used to detect the temporal changes of the number of controlling parameters in a dynamical process, for example, geomagnetic fluctuation through time. By means of sliding-window correlation-dimension analyses of total-field fluctuations at three geomagnetic ground stations in Taiwan, a decrease in correlation dimension during storms has been confirmed in this paper. Such a decrease in the correlation dimension strongly indicates shrinking of phase space in the geomagnetic dynamical system, while the hidden, degenerated state variable remains inconclusive and more work is needed to address this issue.
Highlights
Since the emergence of the concept of nonlinear dynamics in the 1970s, the idea of geomagnetic attractor is no longer fanciful
TAO, Vol 16, No 2, June 2005 geomagnetic auroral electrojet AE index, a measure of overall geomagnetic activity in the auroral region derived from ground station measurements of north-south magnetic field components, and presented two different correlation dimensions of the AE index, i.e., 3.6 for the former and 2.4 for the latter
In contrast to the AE index, Roberts et al (1991) used a data set containing 40,000 values of the western auroral electrojet AL index with the sampling interval of 2.5 minutes. They extracted several relatively quiet segments of 1,000 data points from the raw time series compiled by Bargatze et al (1985), and found a correlation dimension of 4.0 for AL data, which is higher than the estimates of Vassiliadis et al (1990) and Shan et al (1991)
Summary
Since the emergence of the concept of nonlinear dynamics in the 1970s, the idea of geomagnetic attractor is no longer fanciful. Very recently, Sitnov et al (2000) proposed a hybrid catastrophe model of a magnetospheric substorm (Smith et al 1986; Goertz and Smith 1989) that behaves like a nonequilibrium phase transition with features of both first- and second-order phase transitions They have found that the effective dimension of a dynamical magnetospheric system degenerates during substorms and, based on their singular spectrum analysis, dynamic trajectory lies on a twodimensional surface in the three-dimensional space of the main eigenvectors. In this case, while the actual dimension associated with a substorm or storm is still a subject of debate (Klimas et al 1996), it is worth considering if it is possible to observe the temporal variation in the correlation dimension of the geomagnetic system during a storm. A discussion relating to some of the relevant physical problems in the magnetospheric dynamics will be provided at the end of this paper
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