On modelling of artificial networks arising in applications

We consider systems of two ordinary differential equations, which describe two-component Genomic Networks (GRN) and VNT (Virtual Network Topology) - controlled two dimensional telecommunication networks. VNT control over network is based on attractor selection like in biological (genomic) networks. We show that besides a set of stable critical points an attractor can be in the form of a stable periodic regime. We show the mechanism of emergence of a limit cycle through the Andronov-Hopf bifurcation. Similar attractors can appear in mathematical models with no limitations on dimensionality.