Abstract. The ring current growth and decay, characterized by the D_st index, has been studied for thirty years using the Burton et al. (1975) equation. The original formula is based on the restriction of the DPS (Dessler, Parker, and Schoppke) theorem and assuming a constant decay time of particles. The decay time scale is important because the energy injection rate cannot be determined it without the knowledge of this parameter. In a previous work, instead of using a constant value, we introduced the decay time of particles in the energy rate balance equation as a continuous function of the absolute value of the pressure corrected D_st index to avoid the reported discontinuities determining it. Here, based on the DPS restriction, we extend our previous empirical work to obtain analytically the proposed continuous function considering losses due to a global resistive force as a product of viscous-like, and other related dissipation processes. We test our model predicting D_st for a couple of specific storm events and also comparing our results with forecasts of a good reference model appeared in the literature.