Perceptual decision-making plays a pivotal role in cognitive tasks. Over the past several decades, mathematical models, based on experimental studies, have been developed for simple two-alternative decision tasks. A best-known class of models is the drift-diffusion models, which have been quite successful in fitting most aspects of response time and accuracy data from two-alternative reaction-time tasks. Thesemodels, however, are phenomenological: they are not based on physiology underlying perceptual decision processes. A more biologically-realistic reduced two-variable model, based on decision-making neurophysiology, has been recently proposed, which can replicate and reproduce most of the features of the psychophysical and neuronal data.
In this dissertation, we conduct a thorough mathematical analysis of the mechanisms underlying the simple perceptual decision making processes by studying the biological-plausible reduced model and drift-diffusion models.
First, we give a detailed analysis of drift-diffusion models. Second, we find precise conditions on parameters for when the biophysical-based two-dimensional model can be rigorously reduced to a one-dimensional diffusion model, Third, we provide precise estimates on the parameter values so that the biophysical-based model can be controlled to reproduce the psychological experimental data.