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Basal ganglia oscillations: The role of delays and external excitatory nuclei

Basal ganglia are interconnected deep brain structures involved in movement generation. Their beta-band oscillations (13-30Hz) are known to be linked to Parkinson's disease motor symptoms. In this paper, we provide conditions under which these oscillations may occur, by explicitly considering the role of the pedunculopontine nucleus (PPN). We analyze the existence of equilibria in the associated firing-rate dynamics and study their stability by relying on a delayed MIMO frequency analysis. These results are illustrated with simulations that confirm numerically the analytic predictions of our two main theorems.