Transmission of stimulus-locked responses in two coupled phase oscillators.

A model of two n:m coupled phase oscillators is studied, where both oscillators are subject to random forces, but only one oscillator is repetitively stimulated with a pulsatile stimulus. The focus of the paper is on transmission of transient responses as well as transient synchronization and desynchronization, which are stimulus locked, i.e., tightly time locked to the stimulus. A bistability or multistability of stable synchronized states of the two-phase oscillators (modulo 2pi ) occurs due to the n:m coupling. Accordingly, after stimulation the two oscillators may tend to qualitatively different stable states, which leads to a cross-trial (CT) response clustering (i.e., a switching between qualitatively different poststimulus responses across trials) of either one of the oscillators or both. A stochastic CT phase resetting analysis allows one to detect such transient responses and provides a reliable estimation of the transmission time. In contrast, CT averaging (averaging over an ensemble of responses), CT standard deviation, and CT cross correlation fail in studying the transmission of such stimulus-locked responses, even in the simpler case of 1:1 coupling. In particular, even though being used as golden standard for the analysis of evoked responses in medicine and neuroscience, CT averaging typically causes severe artifacts and misinterpretations.