Attracting sets in network regulatory theory

Modern telecommunication networks are very complex and they should be able to deal with rapid and unpredictable changes in traffic flows. Virtual Network Topology is used to carry IP traffic over Wavelength-division multiplexing optical network. To use network resources in the most optimal way, there is a need for an algorithm, which will dynamically re-share resources among all devices in the particular network segment, based on links utilization between routers. Attractor selection mechanism could be used to dynamically control such Virtual Network Topology. The advantage of this algorithm is that it can adopt to very rapid, unknown and unpredictable changes in traffic flows. This mechanism was adopted from biology - gene regulatory networks in cells use it to adopt to unknown changes in the environment. The dynamical system modeling the gene regulatory network is considered. The relations between genes are described by the regulatory matrix W with the entries from the set {−1, 0, 1} meaning inhibition, no relation and activation respectively. The structure of the attracting set in some specific case is studied. It is remarkable that the attracting set contains a focus-type critical point.