Stochastic phase resetting of stimulus-locked responses of two coupled oscillators: transient response clustering, synchronization, and desynchronization.

Transient phase dynamics, synchronization, and desynchronization which are stimulus-locked (i.e., tightly time-locked to a repetitively administered stimulus) are studied in two coupled phase oscillators in the presence of noise. The presented method makes it possible to detect such processes in numerical and experimental signals. The time resolution is enormous, since it is only restricted by the sampling rate. Stochastic stimulus locking of the phases or the n:m phase difference at a particular time t relative to stimulus onset is defined by the presence of one or more prominent peaks in the cross-trial distribution of the phases or the n:m phase difference at time t relative to stimulus onset in an ensemble of poststimulus responses. The oscillators' coupling may cause a transient cross-trial response clustering of the poststimulus responses. In particular, the mechanism by which intrinsic noise induces symmetric antiphase cross-trial response clustering in coupled detuned oscillators is a stochastic resonance. Unlike the presented approach, both cross-trial averaging (where an ensemble of poststimulus responses is simply averaged) and cross-trial cross correlation (CTCC) lead to severe misinterpretations: Triggered averaging cannot distinguish a cross-trial response clustering or decorrelation from a mean amplitude decrease of the single responses. CTCC not only depends on the oscillators' phase difference but also on their phases and, thus, inevitably displays "artificial" oscillations that are not related to synchronization or desynchronization.