title: Effective desynchronization with bipolar double-pulse stimulation.
abstract: This paper is devoted to the desynchronizing effects of bipolar stimuli on a synchronized cluster of globally coupled phase oscillators. The bipolar pulses considered here are symmetrical and consist of a positive and a negative monopolar pulse. A bipolar single pulse with the right intensity and duration desynchronizes a synchronized cluster provided the stimulus is administered at a vulnerable initial phase of the cluster's order parameter. A considerably more effective desynchronization is achieved with a bipolar double pulse consisting of two qualitatively different bipolar pulses. The first bipolar pulse is stronger and resets the cluster, so that the second bipolar pulse, which follows after a constant delay, hits the cluster in a vulnerable state and desynchronizes it. A bipolar double pulse desynchronizes the cluster independently of the cluster's dynamical state at the beginning of the stimulation. The dynamics of the order parameter during a bipolar single pulse or a bipolar double pulse is different from the dynamics during a monopolar single pulse or a monopolar double pulse. Nevertheless, concerning their desynchronizing effects the monopolar and the bipolar stimuli are comparable, respectively. This is significant for applications where bipolar stimulation is required. For example, in medicine and physiology charge-balanced stimulation is typically necessary in order to avoid tissue damage. Based on the results presented here, demand-controlled bipolar double-pulse stimulation is suggested as a milder and more efficient therapy compared to the standard permanent high-frequency deep brain stimulation in neurological patients.