Binocular rivalry entails a perceptual alternation between incompatible stimuli presented to the two eyes. A minimal explanation for binocular rivalry involves strong competitive inhibition between neurons responding to different monocular stimuli to preclude simultaneous activity in the two groups. In addition, strong self-adaptation of dominant neurons is necessary to enable suppressed neurons to become dominant in turn. Here a minimal nonlinear neural model is developed incorporating inhibition, self-adaptation, and recurrent excitation. The model permits derivation of an equation for mean dominance duration as a function of the underlying physiological variables. The dominance duration equation incorporates an explicit representation of Levelt's second law. The same equation also shows that introduction of a simple compressive response nonlinearity can explain Levelt's fourth law. Finally, addition of brief, recurrent synaptic facilitation to the model generates properties of rivalry memory.