Effective desynchronization with a resetting pulse train followed by a single pulse

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Abstract
A combined pulse train, single-pulse stimulation technique is presented here which makes it possible to effectively desynchronize a cluster of globally coupled phase oscillators in the presence of noise. Such a composite stimulus consists of a resetting short periodic high-frequent pulse train followed by a desynchronizing single pulse. The pulse train entrains and, thus, restarts the collective oscillation independently of its initial dynamic state. With a fixed delay after the pulse train, a single pulse is delivered which desynchronizes the cluster by hitting it in a vulnerable state. After the desynchronization the cluster wants to become synchronized again since the incoherent state is unstable. Nevertheless, repeated administration of the same composite stimulus blocks the resynchronization. Compared to double-pulse phase resetting and with regard to neurological applications, this method is particularly mild and can be applied to effectively maintain incoherency in a population of oscillatory neurons that tend to synchronize their ring. The composite stimulation approach sheds new light on the mechanism of standard deep brain stimulation and suggests an improved, milder and demand-controlled deep brain stimulation technique for patients with Parkinson's disease or essential tremor.