The use of low-dimensional materials is a promising approach to improve the key charac- teristics of memristors. The development process includes modeling, but the question of the most common compact model applicability to the modeling of device characteristics with the inclusion of low-dimensional materials remains open. In this paper, a comparative analysis of linear and nonlinear drift as well as threshold models was conducted. For this purpose, the assumption of the relationship between the results of the optimization of the volt–ampere characteristic loop and the descriptive ability of the model was used. A global random search algorithm was used to solve the optimization problem, and an error function with the inclusion of a regularizer was developed to estimate the loop features. Based on the characteristic features derived through meta-analysis, synthetic volt–ampere characteristic contours were built and the results of their approximation by different models were compared. For every model, the quality of the threshold voltage estimation was evaluated, the forms of the memristor potential functions and dynamic attractors associated with experimental contours on graphene oxide were calculated.