The research involves the study of auditory-evoked potentials (AEPs) recorded using electroencephalography (EEG) from human subjects. The study aims to mathematically model how the brain responds to the audio stimulus, which involves the identification of differences in the AEPs by simulating binaural hearing. This is achieved by transmitting auditory stimulus in-phase in both ears, and tones which are 180 degrees out of phase in each ear. The study creates a range of models with the aim to determine the type and order of the models which provide the best fit to the AEPs, and to analyze the differences between the homo-phasic and anti-phasic models. The work discovered that multi-input single-output (MISO) transfer function models are able to fit the AEPs. Tenth-order models provide optimal mathematical fit; these models produced significantly greater fit than lower order models while higher order models produce minimal improvement. The addition of zeros also produced insignificant improvement upon the mathematical fit. About 75-95% of mathematical fits were achieved across all subjects. Analysis of the pole-zero plots suggest that the pole pairs with frequencies greater than 125 rad/s are more damped for the trials using homo-phasic auditory stimulus compared with models generated for trials using anti-phasic stimulus. This suggests that if the brain is processing binaural hearing, then the high-frequency poles in 10-pole MISO transfer functions should have low damping.