5. Results

[15]  We applied the algorithm to a 5 minute sample of TV auroral observations made at Lovozero station. The date of observation was 11 January 1998, 0027 LT. At this time there was a bright stable arc on the edge of the sky near to the horizon, and pulsating patches occurred in the center of the image. These patches, usually appearing after the brightening of arcs, were the objects of our interest.

Figure 1

[16]  The TV recordings were digitized on typical PC equipment with a speed 5 of images per second and a resolution of 128 128. The central part of the image ( 100 100 ) was cut out. The digitized sequence of images contained 1497 images. The corresponding keograms in north-south and east-west directions are shown in Figure 1.

[17]  Autocorrelation functions from temporary dependence of integrated intensity on complete image and by its central part ( 20 20 pixels) were designed to define the quantization step t for (1). Both autocorrelation functions have the first minimum at ~4 s (18-20 steps of digitizing). Therefore, for further calculation of correlation integrals we shall use t = 1 s.

[18]  We found that for these data the gray level 13 is the best to investigate the dynamics of pulsations. For smaller levels the influence of noise is strong. For larger levels the area of luminosity is strongly granulated.

[19]  The results of the calculation of correlation integrals on the complete image for embedding dimensions d from 2 up to 18 are shown in Figure 2a. For 0.001 < C (r) < 0.1 the dependence of lnC(r) on lnr has been linearly approximated by the least squares method. The dependence of the slope of the graph on d is shown in Figure 2b. It is evident that the slope of the graph varies a little, and even for d=18 has a value ~7.0.

Figure 2

Figure 3

[20]  Figure 3 presents the results of similar calculations, but for the central ( 20 20 ) part of the image. The dependence C(r) has a somewhat different shape. For large d there are two linear parts in the graph. The dependence of slopes of the diagram on d in these parts, calculated by the least squares method, are shown in Figure 3b. For larger-scale changes in the image the correlation dimension is close to 2, which is the usual characteristic of periodic modes. However, these oscillations are superimposed on small-scale variations with more complex dynamics (correlation dimension ~5.0-5.5).

[21]  The values of correlation dimensions obtained here suggest that the dynamics of the whole area filled by luminosity in the TV image is characterized by a dimension of seven. In other words, the attractor (the phase trajectory) of the system has a dimension of seven. When we select an area filled mainly by one patch, we basically extract the two-dimensional part, on which there are smaller variations in other dimensions, from the seven-dimensional attractor.