Two model neural populations — one driven by the left eye's image, one by the right — each report a firing rate r that competes for perceptual dominance through reciprocal (cross) inhibition, following Wilson's rate-based rivalry model (Wilson, PNAS 2003):
τ_r · dr_i/dt = −r_i + f( I_i − β·r_j − g·a_i + n_i(t) )
τ_a · da_i/dt = −a_i + r_i
f(x) = 1 / (1 + e^(−k(x − θ))) [sigmoid firing-rate response]
r_i is the population's firing rate, a_i is a slow spike-frequency adaptation variable that fatigues whichever population has been winning, β sets how strongly the two populations suppress each other, and n_i(t) is independent noise in each population. When one population's rate rises it inhibits its rival — but its own adaptation variable slowly grows, weakening it until the rival, freed from inhibition, takes over. This inhibition–adaptation cycle is what makes the dominant percept spontaneously and irregularly flip every few seconds, exactly as it does with real binocular rivalry (e.g. viewing different images in each eye through a stereoscope).
- Mutual inhibition β — how hard the dominant population suppresses its rival. Too low and both percepts blend/co-dominate; realistic rivalry needs β large enough to force one winner at a time.
- Adaptation strength g — how quickly the winning population fatigues. Higher g means faster, more frequent switches.
- Neural noise σ — random fluctuations that can trigger an early switch even before adaptation would force one; rivalry switch timing is close to a noisy, roughly gamma-distributed process, not a metronome.
- Contrast bias — makes one eye's stimulus objectively stronger, biasing (but not eliminating) rivalry — matching Levelt's proposition that stimulus strength shifts the fraction of time a percept dominates.
The top panel overlays the two rival images: each one's opacity tracks its population's live firing rate r_i, so the image that currently "wins" visibly emerges while the other fades — mirroring what a real observer reports seeing. The bottom panel plots both firing rates over time, so you can watch the alternating dominance emerge directly from the coupled ODEs.