Physica 25D (1987) 165-172 North-Holland, Amsterdam AN ATrRACTOR IN A SOLAR TIME SERIES J. KURTHS Central Institute for Astrophysics, Academy of Sciences of the GDR, 1500 Potsdam, GDR and H. HERZEL Department of Physics, Humboldt University Berlin, GDR Received 30 October 1985 Revised manuscript received 8 April 1986 A time series analysis of observed solar radio pulsations suggests that there must be a low-dimensional attractor. The power spectrum cannot be interpreted as a superposition of periodic components. Estimates of the maximum Lyapunov exponent and of the Kolmogorov entropy give some indications for a deterministic chaos. In order to study the limitations inherent in small data samples we include data from the Lorenz model and an artificial noise record. Consequences for the physical modelling of the pulsation event are discussed. 1. Introduction Geophysical and astrophysical research rely on experimental data. In contrast to other fields of physics it is generally not possible to influence the medium under consideration or to repeat an ob- servation under the same co~aditions. Nevertheless, measurements play an important role in modelling the physical processes involved. Usually, the correlation analysis and the spec- tral analysis are applied to the data [1], which is connected with the physical concept of mode in linear theories. New methods for the description of dynamical systems (in particular of the de- terministic chaos) have been developed. The con- cept of mode has been supplemented by other quantities such as dimension, Lyapunov expo- nents and the Kolmogorov entropy. Recently, al- gorithms have been proposed to estimate these quantities from measurements [2]. Here, we report observations of solar radio radi- ation exhibiting a pulsating structure, which is a specific manifestation of solar activity. The pres- ent paper deals with these measurements. Both concepts of time series analysis are used to obtain some aids for modelling the physical background mechanism. In section 2 we introduce the data. Section 3 deals with the spectral analysis. Estimates of the attractor dimension are treated in section 4. Further basic properties of an attractor, such as the maximum Lyapunov exponent and the Kolmogorov entropy, are discussed in section 5. Section 6 contains an interpretation of our results. 2. Observations The variation of the solar electromagnetic radia- tion and the particle emission is mainly caused by solar active regions. Solar radio emission in the dm-m wave range provides information about the physical processes in the chromosphere and the corona. Flares are the most violent manifesta- 0167-2789/87/$03.50 © Elsevier Science Publishers B.V. (North-Holland Physics Publishing Division)