The paper is devoted to experimental studies of new methods of cognitive modeling by testing them on a variety of artificially created cognitive models. The features of the process of obtaining such models are studied, and the concepts of a formal cognitive map and a formal cognitive model are introduced. An approach to generating a formal cognitive map with given characteristics, based on the use of random graph models, is proposed and partially formalized. A modification of the configuration model has been carried out, and examples of generating formal fuzzy cognitive maps based on it are given. The architecture of a software solution aimed at supporting experimental research in cognitive modeling is described. Directions for further research, both theoretical and applied in nature, are formulated.