In this article, we derive unique stochastic nonlinear coupled oscillator models of EEG signals from an Alzheimer's Disease (AD) study. EEG signals recorded during resting eyes-open (EO) and eyes-closed (EC) conditions in a pilot study with AD patients and age-matched healthy control subjects (CTL) are employed. An optimization scheme is then utilized to match the output of the stochastic Duffing - van der Pol double oscillator network with EEG signals recorded during each condition for AD and CTL subjects. The selected decision variable are the model parameters and noise intensity. While, the selected signal characteristics are power spectral densities in major brain frequency bands and Shannon and sample entropies to match the signal information content and complexity. It is shown that statistically significant unique models represent the EC and EO conditions for both CTL and AD subjects. Moreover, the inclusion of sample entropy in the optimization process significantly enhances the stochastic nonlinear oscillator model performance. The study suggests that EEG signals recorded under different brain states as well as those belonging to a brain disorder such as Alzheimer's disease can be uniquely represented by stochastic nonlinear oscillators paving the way for identification of new discriminants.