  In this work it is described how to enhance and generalize the equivalent
model (arXiv:0802.0421) of integrate-and-fire dynamics in order to treat any
complex neuronal networks, especially those exibiting modular structure. It has
been shown that, though involving only a handful of equivalent neurons, the
modular equivalent model was capable of providing impressive predictions about
the non-linear integrate-and-fire dynamics in two hybrid modular networks. The
reported approach has also allowed the identification of the causes of
transient spiking confinement within the network communities, which correspond
to the fact that the little activation sent from the source community to the
others implies in long times for reaching the nearly-simultaneous activation of
the concentric levels at the other communities and respective avalanches.
Several other insights are reported in this work, including the smoothing of
the spiking functions, the consideration of intra-ring connections and its
effects, as well as the identification of how the weights in the equivalent
model change for different source nodes. This work has paved the way for a
number of promising developments, which are identified and discussed.
Preliminary results are also described which reveal waves induced by the
integrate-and-fire dynamics along the steady-state regime.
