It is known that cortical networks operate on the edge of instability, in which oscillations can appear. However, the influence of this dynamic regime on performance in decision making, is not well understood. In this work, we propose a population model of decision making based on a winner-take-all mechanism. Using this model, we demonstrate that local slow inhibition within the competing neuronal populations can lead to Hopf bifurcation. At the edge of instability, the system exhibits ambiguity in the decision making, which can account for the perceptual switches observed in human experiments. We further validate this model with fMRI datasets from an experiment on semantic priming in perception of ambivalent (male versus female) faces. We demonstrate that the model can correctly predict the drop in the variance of the BOLD within the Superior Parietal Area and Inferior Parietal Area while watching ambiguous visual stimuli.