  In this work, we study the dynamic range of a neuronal network of excitable
neurons with excitatory and inhibitory synapses. We obtain an analytical
expression for the critical point as a function of the excitatory and
inhibitory synaptic intensities. We also determine an analytical expression
that gives the critical point value in which the maximal dynamic range occurs.
Depending on the mean connection degree and coupl\-ing weights, the critical
points can exhibit ceasing or ceaseless dynamics. However, the dynamic range is
equal in both cases. We observe that the external stimulus mask some effects of
self-sustained activity (ceaseless dynamic) in the region where the dynamic
range is calculated. In these regions, the firing rate is the same for
ceaseless dynamics and ceasing activity. Furthermore, we verify that excitatory
and inhibitory inputs are approximately equal for a network with a large number
of connections, showing excitatory-inhibitory balance as reported
experimentally.
