This article addresses methodical issues concerning the modeling of the Dst variation in a geomagnetic storm. We describe the so-called RBM (Russell — Burton — McPherron) model representing an ordinary differential equation with solutions simulating the relation between the Dst variation and the azimuthal component of the interplanetary electric field. Special attention is paid to the threshold nature of Dst variation excitation. We would like to emphasize the necessity of stochastic extension of the RBM model by taking into account fluctuations inherent to any physical system. The integral representation of a Dst variation bifurcation diagram is given. It enables us to account for the effect of fluctuations that eliminate the diagram root singularity and cause a threshold point shift. The Dst variation is shown to be typical of the wide class of threshold phenomena similar to second-order phase transitions. We draw an analogy with threshold phenomena in Earth’s magnetosphere, atmosphere, and lithosphere. In addition, we briefly discuss the issue about soft and hard passages through the threshold, as well as about explosive instability in geophysical media.