Mathematical Model of Network and Communication Node State in TensorField Algebraic Space Subject to Electromagnetic Pulse Lesion

Abstract

The possibility of applying a tensor approach to the mathematical model construction of the network and communication node state in the algebraic space of tensor field is proposed, taking into account the factors of destructive impact by an electromagnetic pulse (EMP) causing functional damage to the structural elements of communication equipment (routers, controls, computing equipment and monitoring) of networks and communication nodes. To construct the specified mathematical model under conditions of destructive influence, taking into account the provisions of network tensor analysis, a 2-simplex structure at the router level is introduced: a set of closed and open paths connecting nodes with N possible connections in total. The whole set of structures is considered as a particular coordinate system within N-dimensional space, corresponding to various ways of connecting N branches, while maintaining their original number or moving from one set of independent paths to another within the analyzed space without loss of quality and performance characteristics of the communication equipment of networks and communication nodes. Taking into account the size, quantity of source data and multi-criteria, the solution of problems of optimizing the characteristics, properties and structure of a communication system that is subject to destructive influence, including networks and routing nodes, is carried out in parts, iteratively involving special methods. In future, the use of this model at the stage of the network and communication node parameter optimizing will allow to account them in the benefit of protection from negative (destructive) impact threats, followed by the mathematical model formation to ensure functional stability of networks and communication nodes of critical purpose.