In this work, we study the dynamic range (DR) 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 DR occurs. Depending on the mean connection degree and coupling weights, the critical points can exhibit ceasing or ceaseless dynamics. We observe that the external stimulus masks some effects of self-sustained activity (ceaseless dynamic) in the region where the DR is calculated. In these regions, the firing rate is the same for ceaseless dynamics and ceasing activity. In addition to studying the DR enhancement on the criticality for a random network we apply the model in cortical microcircuits.

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