Perceptual bistability arises when two conflicting interpretations of an ambiguous stimulus or images in binocular rivalry (BR) compete for perceptual dominance. From a computational point of view, competition models based on cross-inhibition and adaptation have shown that noise is a crucial force for rivalry, and operates in balance with adaptation. In particular, noise-driven transitions and adaptation-driven oscillations define two dynamical regimes and the system explains the observed alternations in perception when it operates near their boundary. In order to gain insights into the microcircuit dynamics mediating spontaneous perceptual alternations, we used a reduced recurrent attractor-based biophysically realistic spiking network, well known for working memory, attention, and decision making, where a spike-frequency adaptation mechanism is implemented to account for perceptual bistability. We thus derived a consistently reduced four-variable population rate model using mean-field techniques, and we tested it on BR data collected from human subjects. Our model accounts for experimental data parameters such as mean time dominance, coefficient of variation, and gamma distribution fit. In addition, we show that our model operates near the bifurcation that separates the noise-driven transitions regime from the adaptation-driven oscillations regime, and agrees with Levelt’s second revised and fourth propositions. These results demonstrate for the first time that a consistent reduction of a biophysically realistic spiking network of leaky integrate-and-fire neurons with spike-frequency adaptation could account for BR. Moreover, we demonstrate that BR can be explained only through the dynamics of competing neuronal pools, without taking into account the adaptation of inhibitory interneurons. However, the adaptation of interneurons affects the optimal parametric space of the system by decreasing the overall adaptation necessary for the bifurcation to occur, and introduces oscillations in the spontaneous state