  Many neuronal systems and models display a certain class of mixed mode
oscillations (MMOs) consisting of periods of small amplitude oscillations
interspersed with spikes. Various models with different underlying mechanisms
have been proposed to generate this type of behavior. Stochastic versions of
these models can produce similarly looking time series, often with noise-driven
mechanisms different from those of the deterministic models. We present a suite
of measures which, when applied to the time series, serves to distinguish
models and classify routes to producing MMOs, such as noise-induced
oscillations or delay bifurcation. By focusing on the subthreshold
oscillations, we analyze the interspike interval density, trends in the
amplitude and a coherence measure. We develop these measures on a biophysical
model for stellate cells and a phenomenological FitzHugh-Nagumo-type model and
apply them on related models. The analysis highlights the influence of model
parameters and reset and return mechanisms in the context of a novel approach
using noise level to distinguish model types and MMO mechanisms. Ultimately, we
indicate how the suite of measures can be applied to experimental time series
to reveal the underlying dynamical structure, while exploiting either the
intrinsic noise of the system or tunable extrinsic noise.
