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Deep brain stimulation (DBS) is a widely applied clinical procedure for the alleviation of pathological neural activity, and is particularly effective in suppressing the symptoms of Parkinson's disease. The mechanisms of action of DBS remain to be fully elucidated. In this paper, we present an application to DBS of the concepts of dither injection and equivalent nonlinearity from the theory of nonlinear feedback control systems. We propose that this model provides a framework for understanding the mechanism by which an injected high-frequency signal can quench undesired oscillations in closed-loop systems of interacting neurons in the brain.