Noise and critical behavior of the pupil light reflex at oscillation onset

We have induced oscillations in the human pupil light reflex using two different kinds of external electronic feedback: smooth negative feedback (SNF) and piecewise constant negative feedback (PCNF). The behavior of the mean amplitude and period at oscillation onset are shown to be in good agreement with a model of this neural system incorporating the external feedback. The critical behavior displayed through amplitude and period fluctuations is different in each case. The observation that amplitude fluctuations are larger (smaller) than period fluctuations for SNF (PCNF) is explained theoretically and by numerical integration of a stochastic delay-differential equation with additive and multiplicative colored noise. We find that both types of noise postpone the Hopf bifurcation in SNF by an amount proportional to the noise intensity and inversely proportional to the correlation time. The implications for analyzing bifurcations in neural systems are discussed.