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Growing evidence suggests that synchronized neural oscillations in the cortico-basal ganglia network may play a critical role in the pathophysiology of Parkinson's disease. In this study, a new model of the closed loop network is used to explore the generation and interaction of network oscillations and their suppression through deep brain stimulation (DBS). Under simulated dopamine depletion conditions, increased gain through the hyperdirect pathway resulted in the interaction of neural oscillations at different frequencies in the cortex and subthalamic nucleus (STN), leading to the emergence of synchronized oscillations at a new intermediate frequency. Further increases in synaptic gain resulted in the cortex driving synchronous oscillatory activity throughout the network. When DBS was added to the model a progressive reduction in STN power at the tremor and beta frequencies was observed as the frequency of stimulation was increased, with resonance effects occurring for low frequency DBS (40 Hz) in agreement with experimental observations. The results provide new insights into the mechanisms by which synchronous oscillations can arise within the network and how DBS may suppress unwanted oscillatory activity.