Resting state fMRI has been the primary tool for studying the functional organization of the human brain. However, even at so-called "rest", ongoing brain activity and its underlying physiological organization is highly dynamic and yet most of the information generated so far comes from group analysis. Here we developed an imaging-based technique capable of portraying information of local dynamics at a single-subject level reliably by using a whole-brain model that estimates a local bifurcation parameter, which reflects if a brain region presents stable, asynchronous or transitory oscillations. Using 50 longitudinal resting state sessions of one single subject and single resting state sessions from a group of 50 participants we demonstrated that individual global and local brain dynamics can be estimated consistently with respect to a reference group using only a scanning time of 15 to 20 minutes. We also showed that brain hubs are closer to a transition point between synchronous and asynchronous oscillatory dynamics and that dynamics in frontal areas have larger variations compared to other regions. Finally, we analyzed the variability and error of these dynamics and found high symmetry between hemispheres, which interestingly was reduced by adding more sessions. The framework presented here can be used to study functional brain dynamics on an individual level, opening new avenues for possible clinical applications.