Complex Oscillations in the Human Pupil Light Reflex with “Mixed” and Delayed Feedback*

Simple periodic as well as more complex behaviors are shown to occur in the human pupil light reflex with piecewise constant mixed and delayed feedback. The output of an infrared video pupillometer, an analog voltage proportional to pupil area, is processed by an electronic comparator which synthesizes the piecewise constant feedback. The system is described by a nonlinear delay differential equation which has been previously shown analytically to exhibit periodic and aperiodic behavior. After parameter estimation from the data, it is found that the observed simple periodic behaviors correlate well with the model behaviors, Although more complex behavior can be observed for parameter values which gave complicated dynamics in the model, there is not a one-to-one correspondence between the observed and predicted results. The effect of uncontrollable fluctuations in the parameters on the observability of complex dynamics in this system is discussed.