Up states are the best studied example of an emergent neural dynamic regime. Computational models based on a single class of inhibitory neurons indicate that Up states reflect bistable dynamic systems in which positive feedback is stabilized by strong inhibition and predict a paradoxical effect in which increased drive to inhibitory neurons results in decreased inhibitory activity. To date, however, computational models have not incorporated empirically defined properties of parvalbumin (PV) and somatostatin (SST) neurons. Here we first experimentally characterized the frequency-current (F-I) curves of pyramidal (Pyr), PV, and SST neurons from mice of either sex, and confirmed a sharp difference between the threshold and slopes of PV and SST neurons. The empirically defined F-I curves were incorporated into a three-population computational model that simulated the empirically derived firing rates of pyramidal, PV, and SST neurons. Simulations revealed that the intrinsic properties were sufficient to predict that PV neurons are primarily responsible for generating the nontrivial fixed points representing Up states. Simulations and analytical methods demonstrated that while the paradoxical effect is not obligatory in a model with two classes of inhibitory neurons, it is present in most regimes. Finally, experimental tests validated predictions of the model that the Pyr ↔ PV inhibitory loop is stronger than the Pyr ↔ SST loop.SIGNIFICANCE STATEMENT Many cortical computations, such as working memory, rely on the local recurrent excitatory connections that define cortical circuit motifs. Up states are among the best studied examples of neural dynamic regimes that rely on recurrent excitatory excitation. However, this positive feedback must be held in check by inhibition. To address the relative contribution of PV and SST neurons, we characterized the intrinsic input-output differences between these classes of inhibitory neurons and, using experimental and theoretical methods, show that the higher threshold and gain of PV leads to a dominant role in network stabilization.