Spike patterning of a stochastic phase model neuron given periodic inhibition

We present a phase model of a repetitively firing neuron possessing a phase-dependent stochastic response to periodic inhibition. We analyze the dynamics in terms of a stochastic phase map and determine the invariant phase distribution. We use the latter to compute both the distribution of interspike intervals (ISIs) and the stochastic winding number (mean firing rate) as a function of the input frequency. We show that only low-order phase locking persists in the presence of weak phase dependence, and is characterized statistically by a multimodal ISI distribution and a nonmonotonic variation in the stochastic winding number as a function of input frequency.