A network is considered, which is modelled by a system of ordinary differential equations. The dynamics of a network depends on the attracting sets in a phase space. The problem of control and management of this network is in a focus of our study. The specific case is considered, where attractors are periodic trajectories. We provide the way of controlling the network by changing of a certain group of parameters. The numerical approach combined with the analytical solutions is used. As a by-product, the existence of multiple periodic solutions is proved. They are constructed explicitly for a specific three-dimensional system. Problems of control and management of systems of this kind are challenging issues in the theory of genetic networks.