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Our perception of the world is built from the incoming sensory information that we receive. When this sensory information is ambiguous, or can be associated with multiple conflicting causes, perception often ‘switches’ back and forth between possible states, a phenomenon referred to as ‘perceptual competition’. Most commonly, perceptual competition is studied in the form of binocular rivalry, where conflicting images are presented separately to the two eyes, and observers report ongoing perceptual switching between the images. There is a rich history of modeling the switching phenomena of binocular rivalry, but the relationship between the mechanisms of switching and the networks underlying typical binocular vision and binocular combination have gone mostly unexplored. Here we present a biologically plausible model of binocular combination that is achieved by applying simple connectivity rules to excitatory-inhibitory networks with strong recurrent excitation and stabilizing inhibition. This network model explains a wide array of phenomena in both stable binocular combination and in the oscillatory states characteristic of binocular rivalry, and serves as a foundation for understanding the network structure that underlies binocular visual perception.