  Currently we routinely develop a complex neuronal network to explain observed
but often paradoxical phenomena based upon biological recordings. Here we
present a general approach to demonstrate how to mathematically tackle such a
complex neuronal network so that we can fully understand the underlying
mechanism. Using an oxytocin network developed earlier as an example, we show
how we can reduce a complex model with many variables to a tractable model with
two variables, while retaining all key qualitative features of the model. The
approach enables us to uncover how emergent synchronous bursting could arise
from a neuronal network which embodies all known biological features.
Surprisingly, the discovered mechanisms for bursting are similar to those found
in other systems reported in the literature, and illustrate a generic way to
exhibit emergent and multi-time scale spikes: at the membrane potential level
and the firing rate level.
