Binocular rivalry is what you see when each eye is shown a different image: perception does not blend them — it alternates between one and the other every few seconds, entirely on its own. This is modelled with a reciprocal-inhibition rate model (Wilson 2003; Laing & Chow 2002): two neural populations, one representing each percept, mutually suppress each other while each one is also weakened by its own slow spike-frequency adaptation.
τ dE_i/dt = -E_i + f(I - β·E_j - g·A_i + ξ)
τ_a dA_i/dt = -A_i + E_i
f(x) = 1 / (1 + e^(-4x)) (sigmoid firing-rate response)
E₁, E₂ are the firing rates of the two populations (i, j = 1,2, j≠i); A₁, A₂ are slow adaptation variables that track recent activity and subtract from a population's own drive; β sets how strongly each population suppresses the other; ξ is Gaussian noise. Whichever population is ahead suppresses its rival through β and dominates perception — but the longer it stays active, the more its own adaptation A_i builds up, until adaptation plus noise lets the rival escape inhibition and take over. This adaptation-driven escape is what produces the roughly-periodic alternation seen in real rivalry experiments.
- Input drive I — raises both populations' base excitability (like stimulus contrast); higher I gives faster, more regular switching.
- Mutual inhibition β — how hard the winning percept suppresses the other. Below a critical β, the two rates just settle to a stable mixed state (no switching); above it, alternation appears.
- Adaptation g — how strongly fatigue undermines the dominant population. Larger g shortens each dominance period.
- Noise σ — random fluctuations that can trigger an early switch even before adaptation forces one, matching the variable (not perfectly periodic) dominance durations measured in real rivalry.
Real-world relevance: this exact class of model is used in visual neuroscience to explain not only binocular rivalry but also ambiguous-figure reversals (Necker cube, Rubin's vase) and motion-direction rivalry — cases where a stable external stimulus nonetheless produces a switching subjective percept, one of the clearest empirically tractable windows into the neural correlates of consciousness.