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The dynamics of the intensity of cosmic rays is known to be different on the ascending and descending branches of the 11-year solar cycle, i.e., hysteresis phenomena are observed. Recently, it has been obtained that at shorter intervals on the scale of magnetic storms there are also signs of hysteresis in dependences of cosmic ray cutoff rigidities R (geomagnetic thresholds) on heliosphere and geosphere parameters. R is the rigidity below which a particle flux is cut off due to geomagnetic shielding. In this paper, we have analyzed the dependence of the geomagnetic storm index Dst and the variation of the ΔR thresholds on interplanetary magnetic field (IMF) and solar wind (SW) parameters during the two-step magnetic storm on September 7–8, 2017. We have found hysteresis phenomena in the following paired series: (1) dependences of Dst on SW and IMF parameters, and (2) dependences of ΔR on SW and IMF parameters. We have established that the dependence curves in the storm descending phase (main phase) and ascending phase (recovery phase) do not coincide — hysteresis loops are formed. A specific feature of the storm under study is the second lowering of Dst in the recovery phase. The hysteresis pattern reflects this specific storm dynamics, forming two hysteresis loops in response to the two Dst drops.

The geomagnetic cutoff rigidity of cosmic rays (CRs) is the main factor regulating the arrival of CR particles at a given point on Earth's surface or inside the magnetosphere. To study the relationship between cutoffs and near-Earth space parameters, we have selected the strongest magnetic storm that occurred on March 8–11, 2012 during the CAWSES-II interval, recommended by SCOSTEP for detailed studies of solar-terrestrial relations. We have found the geomagnetic cutoffs by two methods: 1) by trajectory calculations in the magnetic field of the perturbed magnetosphere according to the Ts01 model and 2) by the spectrographic global survey method according to the data from the world network of neutron monitors. The largest drop in the cutoffs (−1.1 GV) obtained by the latter method was observed during the recovery phase of the storm. Apparently, this is due to the influence of the supersubstorms that occurred at that time. The analysis has shown that the closest connection of variations in the cutoffs can be traced with the geomagnetic activity index Dst, which indicates the determining contribution of the ring current to the transport of CRs. In addition, we have found a significant connection with the electromagnetic field parameters (with the Bz component of the interplanetary magnetic field and the azimuthal component of the electric field Ey). The dynamic solar wind parameters practically do not control variations in CR geomagnetic cutoff rigidities.