The experimental study of nonlinear and complex systems relies on the design of specific advanced data analysis tools, which need to be able to identify properties of the dynamics which are often subtle, hidden in chaotic motions, or simply by the noise. In such cases, it is necessary to use appropriate techniques that also need to be benchmarked for a quantitative reliability. These techniques, often based on advanced statistical and mathematical tools, can be then applied on suitable systems to provide important validation or input for theoretical models and numerical simulations.
Solar flares and the Sun-Earth connection. In recent years, the study of solar variability and its influence on Earth has increased, both because of a more compelling need for a good protection against solar storms that arise from the massive use of the modern technology, and for the exponential quantitative and qualitative increase of measurements available. Our approach is based on the exploitation of in-situ and remote measurements of the Sun-Earth system, including remote solar imaging, magnetic field, and energetic particles, and solar wind and magnetospheric in situ and remote measurements. The main research topics concern the dynamics of the solar active regions and their relationship with flaring activity through the analysis of the complexity of the magnetic field configuration in flaring active regions [Sorriso-Valvo et al., 2015]. Other studies concern the interpretation in terms of coupling models is also studied from data, for example through the analysis of proper modes [Vecchio et al., 2005].
Geophysical time series analysis. Several geophysical systems can be studied in the framework of complex systems and nonlinear dynamics. Examples are: earthquakes [Carbone et al., 2005], geomagnetic field reversals [Carbone et al., 2006], geomagnetic activity. These phenomena often can be observed as time series, which can be thus studied using, e.g., statistical tools. Their description is useful to validate theoretical models, to advance the general knowledge of the process, and to some extent to help improving the predictability of catastrophic events. Time series of various phenomena are studied and their statistical properties assessed.