On hypothetical gene networks

We study hypothetical gene networks (HGN), which are used in mathematical modeling in information biology. We mainly study symmetric HGN of class $1$, called $M(n,k)$ models. The results obtained support the well-known $(n,k)$-criterion that postulates the existence of stable limit solutions of the autonomous systems considered. In many respects the methods for investigating $M(n,k)$ can be extended to symmetric HGN of other classes.