The Duffing oscillator: a model for the dynamics of the neuronal groups comprising the transient evoked potential

Thirty years ago Zeeman conjectured that the dynamics of the EEG might be modeled by the "equation of motion" of a Duffing oscillator, a pendulum with a nonlinear, cubic, restoring force. In this study the idea is extended to the evoked potential (EP). A transient sensory EP reflects activity from several neuronal groups, pools of neurons that fire in synchrony, with voltage-time curves that overlap appreciably. When the dynamics of each neuronal group is modeled by a Duffing oscillator, multi-electrode transient VEPs are well predicted. Predictions based on Duffing oscillator dynamics are substantially better than those based on the assumption that each neuronal group follows a simpler exponentially damped sinusoid or a function that simulates a post-synaptic potential. The component voltage-time curves are reasonably consistent over 7 subjects, suggesting sequential activation of neuronal groups with delays of several tens of milliseconds between them. The scalp topographies of the components suggest their origins in the occipital cortex.