What are the solar wind parameters that control fluxes of relativistic electrons at GEO?

One of the main questions that arises in the study of a complex dynamical system is: What are the external parameters that govern the evolution of the system? Knowledge of these external parameters is required for both first principle based and data based approaches that study and model the dynamical system. Techniques that identify these input parameters directly from data often rely on dependence measures, such as linear correlation, error reduction ratio, mutual information, and maximal correlation. All of the above, with exception of linear correlation, capture nonlinear dependencies in the dynamical system but lack scalability and often require non-trivial parameter selection to tune the analysis. We study nonlinear dependence measures to find out what solar wind parameters govern the evolution of fluxes of electrons in the energy range 1.8-3.5 MeV at the geostationary orbit. Data from Los Alamos National Laboratory (LANL) geosynchronous energetic particle instrument Energetic Sensor for Particles (ESP) [Reeves et al. 2011] are used in this investigation. The results obtained are discussed in relation to relative importance of the solar wind density and solar wind velocity as control parameters for fluxes of relativistic electrons at GEO.