MODELING THE DYNAMIC INTERACTION PROCESSES USING OF FUZZY TIMED PETRI NETS OF TYPE VF

The dynamic interacting processes modeling is examined in the article, which shows the complex objects operation in the condition of uncertainty. A formalism intended for the development and analysis models of complex parallel and distributed systems is proposed. It is based on the mathematical apparatus of the fuzzy timed Petri nets (FTPN) of type Vf, representing generalized FTPN of type Vf , combining deterministic and non-deterministic character. The algorithm for the functioning FTPN of type Vf is developed. The proposed algorithm provides a solution to the problem of the triggering solvability of transitions occurring in conflict states, the imposition of a fuzzy structure on the network marking with fuzzy composition laws that determine the values the degrees of belonging the input and output transition positions. The model of parallel functioning processing devices is presented in the FTPN form of type Vf. An approach is proposed for modeling dynamic interacting processes based on the matrix theory of Petri nets, that provides an effective form of structure representation, model state dynamics, the space of achievable states, and triggering transitions sequence in the form of vectors and matrices set. On the example of the production model of mechanical processing, it is shown that the accepted triggering transitions rules fully show the functioning FTPN process of type Vf. As a result of the simulation, the reachability tree is obtained as a sequence of matrices.

Cluster Initiatives: Russian Realities and International Experience

The current dynamics of changes in the conditions of state support of cluster initiatives in Russian Federation is analyzed. It is noted that support for the processes of formation and development of clusters in our country is based mainly on political initiatives, but not on the identification of the composition laws of these complex system formations. On the example of international experience the necessity of strengthening the role of science and education institutions in the state-stimulated cluster initiatives, as well as the importance of the formation of advanced training programs for cluster managers and relevant network analytical institutional structures.

Geometric interpretation of Planck-scale-deformed co-products

For theories formulated with a maximally symmetric momentum space we propose a general characterization for the description of interactions in terms of the isometry group of the momentum space. The well known cases of [Formula: see text]-Poincaré-inspired and (2+1)-dimensional gravity-inspired composition laws both satisfy our condition. Future applications might include the proposal of a class of models based on momenta spaces with anti-de Sitter geometry.