  Synaptic noise plays a major role in setting up coexistence of various firing
patterns, but the precise mechanisms whereby these synaptic noise contributes
to coexisting firing activities are subtle and remain elusive. To investigate
these mechanisms, neurons with hybrid synaptic interaction in a balanced
neuronal networks have been recently put forward. Here we show that both
synaptic noise intensity and excitatory weights can make a greater contribution
than variance of synaptic noise to the coexistence of firing states with slight
modification parameters. The resulting statistical analysis of both voltage
trajectories and their spike trains reveals two forms of coexisting firing
patterns: time-varying and parameter-varying multistability. The emergence of
time-varying multistability as a format of metstable state has been observed
under suitable parameters settings of noise intensity and excitatory synaptic
weight. While the parameter-varying multistability is accompanied by
coexistence of synchrony state and metastable (or asynchronous firing state)
with slightly varying noise intensity and excitatory weights. Our results offer
a series of precise statistical explanation of the intricate effect of synaptic
noise in neural multistability. This reconciles previous theoretical and
numerical works, and confirms the suitability of various statistical methods to
investigate multistability in a hybrid synaptic interacting neuronal networks.
