Effective desynchronization with a stimulation technique based on soft phase resetting

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Abstract
A composite stimulation technique is presented here which effectively desynchronizes a cluster of globally coupled phase oscillators in the presence of noise by means of a soft (i.e. slow and mild) reset. A composite stimulus consists of two different stimuli. The first stimulus is a short periodic pulse train, where the entraining frequency is close to the natural frequency of the cluster. In the course of several periods of the collective oscillation, the first stimulus entrains and, hence, resets (restarts) the cluster, independently of its initial dynamic state. With a fixed delay after the first stimulus the second stimulus, a single pulse, is delivered which desynchronizes the cluster by hitting it in a vulnerable state. The desynchronized cluster starts to resynchronize, since the incoherent state is unstable. Resynchronization can, nevertheless, be blocked by repeated administration of the same composite stimulus. Previously designed stimulation techniques use a hard (i.e. abrupt) reset. By contrast, a soft reset makes it possible to effectively desynchronize even if strong, quickly resetting stimuli are not available or not tolerated. Accordingly, this method is particularly mild and can be applied to effectively maintain incoherency in a population of oscillatory neurons which tend to synchronize their firing. The composite stimulation technique can be used i) for an improved, milder and demand-controlled deep brain stimulation for patients with Parkinson's disease or essential tremor and ii) for the manipulation of cerebral information processing by selectively blocking gamma activity.