Recent research has found that the human sleep cycle is characterised by changes in spatiotemporal patterns of brain activity. Yet, we are still missing a mechanistic explanation of the local neuronal dynamics underlying these changes. We used whole-brain computational modelling to study the differences in global brain functional connectivity and synchrony of fMRI activity in healthy humans during wakefulness and slow-wave sleep. We applied a whole-brain model based on the normal form of a supercritical Hopf bifurcation and studied the dynamical changes when adapting the bifurcation parameter for all brain nodes to best match wakefulness and slow-wave sleep. Furthermore, we analysed differences in effective connectivity between the two states. In addition to significant changes in functional connectivity, synchrony and metastability, this analysis revealed a significant shift of the global dynamic working point of brain dynamics, from the edge of the transition between damped to sustained oscillations during wakefulness, to a stable focus during slow-wave sleep. Moreover, we identified a significant global decrease in effective interactions during slow-wave sleep. These results suggest a mechanism for the empirical functional changes observed during slow-wave sleep, namely a global shift of the brain's dynamic working point leading to increased stability and decreased effective connectivity.