The neural correlates of conscious visual perception are commonly studied in paradigms of perceptual multistability that allow multiple perceptual interpretations during unchanged sensory stimulation. What is the source of this multistability in the content of perception? From a theoretical perspective, a fine balance between deterministic and stochastic forces has been suggested to underlie the spontaneous, intrinsically driven perceptual transitions observed during multistable perception. Deterministic forces are represented by adaptation of feature-selective neuronal populations encoding the competing percepts while stochastic forces are modeled as noise-driven processes. Here, we used a unified neuronal competition model to study the dynamics of adaptation and noise processes in binocular flash suppression (BFS), a form of externally induced perceptual suppression, and compare it with the dynamics of intrinsically driven alternations in binocular rivalry (BR). For the first time, we use electrophysiological, biologically relevant data to constrain a model of perceptual rivalry. Specifically, we show that the mean population discharge pattern of a perceptually modulated neuronal population detected in electrophysiological recordings in the lateral prefrontal cortex (LPFC) during BFS, constrains the dynamical range of externally induced perceptual transitions to a region around the bifurcation separating a noise-driven attractor regime from an adaptation-driven oscillatory regime. Most interestingly, the dynamical range of intrinsically driven perceptual transitions during BR is located in the noise-driven attractor regime, where it overlaps with BFS. Our results suggest that the neurodynamical mechanisms of externally induced and spontaneously generated perceptual alternations overlap in a narrow, noise-driven region just before a bifurcation where the system becomes adaptation-driven.