The most probable magnetospheric condition during solar minimum is investigated by using the empirical model of the equatorial proton fluxes presented by Milillo et al. <2001>. The model consists of several segments that reproduce the effects of different physical processes. Those segments describing particle injection and diffusion in the equatorial magnetosphere are considered. The model provides an overall picture of the magnetosphere plasma distributions, thus allowing estimates of the major physical parameters. From this statistical distribution we reconstruct the pattern of the electric field equipotential lines on the equatorial plane. We compute drift paths of test particles at different initial energies and positions, and we focus on both open and closed trajectories and examine through energy-time spectrograms typical features, like dawn-dusk asymmetries of particle transport or flux depletions at specific energies (ion spectral gaps). Some selected parameters of the model are properly varied in order to investigate its possible capability to reproduce different magnetospheric conditions.