Traditionally, brain models rely on parameters fixed across time. While this approach has successfully revealed some key features of brain dynamics, studying the acute effects of drugs may require more flexible modeling approaches. In this context, we used a time-dependent whole-brain model parameterized with a pharmacokinetic equation near a global bifurcation to reproduce large-scale brain dynamics measured with fMRI during intravenous administration of N,N-Dimethyltryptamine (DMT), a short-acting psychedelic drug. Furthermore, in-silico perturbations revealed a transient period of heightened reactivity concentrated in regions correlated with serotonin 5HT2a receptor density, the primary target of psychedelic drugs. These advances suggest a mechanism to explain key features of the psychedelic state and also predict that the temporal evolution of these features aligns with pharmacokinetics. Our results not only contribute to the understanding of how psychedelics transiently affect brain dynamics but also support the implementation of time-dependent parameters in mathematical models of the brain.