Deep brain stimulation (DBS) for Parkinson's disease is a highly effective treatment in controlling otherwise debilitating symptoms yet the underlying brain mechanisms are currently not well understood. We used whole-brain computational modeling to disclose the effects of DBS ON and OFF during collection of resting state fMRI in ten Parkinson's Disease patients. Specifically, we explored the local and global impact of DBS in creating asynchronous, stable or critical oscillatory conditions using a supercritical bifurcation model. We found that DBS shifts the global brain dynamics of patients nearer to that of healthy people by significantly changing the bifurcation parameters in brain regions implicated in Parkinson's Disease. We also found higher communicability and coherence brain measures during DBS ON compared to DBS OFF. Finally, by modeling stimulation we identified possible novel DBS targets. These results offer important insights into the underlying effects of DBS, which may in time offer a route to more efficacious treatments.