Non-linear analysis of the long-term behaviour of solar

The correlation dimension and K-2 entropy of solar filaments are investigated using the Carte Synoptique catalogue of solar filaments from 1919 March to 1989 December. It is found that the correlation dimension of full-disc, low-latitude (<50 degrees) and high-latitude (>= 50 degrees) filament numbers is about 4.05 +/- 0.35, 4.1 +/- 0.45 and 4.0 +/- 0.4, respectively and shows very similar fractal properties when compared with values derived from Wolf sunspot numbers. All K-2 entropies of full-disc, low-latitude and high-latitude filament numbers are positive, though larger than the K-2 entropy of Wolf sunspot numbers. On the basis of the correlation dimension, positive K-2 entropy, chaotic solar dynamo and solar filament-sunspot relationship, it is concluded that the coronal activity of the high layer of the Sun described by solar filament numbers is chaotic and has very complex behaviour.