Abstract. We study the structure of attractors in the two-dimensional dynamical− x2 that appears in the network control theory. We provide description of the attracting set and follow changes this set suffers under the changes of positive parameters µ and Θ.

Abstract-Telecommunication network topologies are changing nowadays. The core telecommunication networks are based on fiber optics infrastructure. WDM technology is used to transmit multiple flows of traffic over a single fiber. Virtual network topology (VNT) is used to route IP traffic over WDM networks. VNT control system must be adaptive to traffic changes and dynamically reconfigure VNT. Langevin equation is used in statistical physics to describe the time evolution of a subset of the degrees of freedom. These degrees of freedom typically are collective (macroscopic) variables changing only slowly in comparison to the other (microscopic) variables of the system. The fast variables are responsible for the stochastic nature of the Langevin equation. Langevin equation could be used to model attractor selection mechanism, which is used by biological systems to adopt to unknown changes in environment. In this paper we describe attractor selection mechanism Simulink model and analyze simulation results.

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