Using nonlinear dynamical techniques, we statistically investigate whether the simulated substorms from global magnetohydrodynamic (MHD) models have a combination of global and multiscale features, revealed in substorm dynamics by Sitnov et al. <2000> and featured the phase transition-like behavior. We simulate seven intervals of total duration of 280 hours from the data set used in the above works <Bargatze et al., 1985>. We analyze the input--output (vBs--pseudo AL index) system obtained from the global MHD model and compare the results to those inferred from the original set (vBs--observed AL index). The analysis of the coupled vBs--pseudo AL index system shows the first-order phase transition map, which is consistent with the map obtained for the vBs--observed AL index system. Although the comparison between observations and global MHD simulations for individual events may vary, the overall global transition pattern during the substorm cycle revealed by singular spectrum analysis (SSA) is statistically consistent between simulations and observations. The coupled vBs--pseudo AL index system also shows multiscale behavior (scale-invariant power law dependence) in SSA power spectrum. Besides, we find the critical exponent of the nonequilibrium transitions in the magnetosphere, which reflects the multiscale aspect of the substorm activity, different from power law frequency of autonomous systems. The exponent relates input and output parameters of the magnetosphere. We also discuss the limitations of the global MHD model in reproducing the multiscale behavior when compared to the real system.