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A comparative analysis of three ground level enhancement (GLE) events—GLE69 (January 20, 2005), GLE71 (May 17, 2012), and GLE72 (September 10–11, 2017)—using hourly integral proton fluxes from GOES (>10, >30, >60 MeV) and 5-min data from high-latitude neutron monitors (Apatity, Oulu, South Pole) is presented. Assuming a power-law integral spectrum, we reconstructed the temporal evolution of the effective spectral index and event amplitude, and extrapolated the spectra to GeV energies. The 2005 event is characterized by a very hard spectrum (γ ≈ 1.5) and a dominant GeV component, whereas the 2012 and 2017 events exhibit softer spectra (γ = 2.0–2.3) and significantly smaller ground-level amplitudes. To quantify the role of the magnetospheric state, variations of the geomagnetic cutoff rigidity Rc were parameterized using the Dst index. We find that cutoff modulation plays a minor role in GLE69, becomes comparable to the intrinsic event amplitude in GLE71, and approaches a controlling factor under near-threshold conditions in GLE72. Using the analytical scaling, it is demonstrated that the Earth's magnetosphere may act as a nonlinear amplifier of transient particle fluxes, with the efficiency of this mechanism increasing for softer spectra. The results define a physical framework describing the transition between acceleration-dominated, mixed, and cutoff-modulated regimes, providing a basis for the classification and interpretation of GLE events. [ABSTRACT FROM AUTHOR] |