The paper deals with the use of extended Petri nets in modeling the processes of extracting rules from neural network components. The mathematical model for extracting rules from neural network components based on a modified timed Petri net is constructed, followed by an analysis of its dynamic behavior based on a timed reachability graph, which is a set of all its states that can be reached when a finite number of transitions are fired. The proposed model allows us to move from the initial detailed structure to its simplified description, which preserves the possibility of obtaining information about the structure and dynamic behavior of the neural network system. The proposed approach can be used in the synthesis of cognitive systems with a neural network organization to provide computational support for the functions of forming, learning, and correcting cognitive networks that display neural network models.