Abstract. Based on the analysis of the problem of cybersecurity we show that its solution is related to the solution of a set of interdependent problems whose features are derived from the topology of cyberspace. We propose a graph, which adequately reflects the topology of the power system computer network for power control of traction substations and its mathematical model as the basis for the creation of contemporary models of cybersecurity. The basis of the developed mathematical model of cybersecurity computer networks is the Pukhov theory of differential transformations. We formalize the criterion of cybersecurity and propose minimax principle for minimization of the functional in the worst combination of flow intensity of cyber attacks and defensive actions. We develop an intelligent method to find the optimal strategy of cyber security computer networks by the extremum analysis of the formalized functional.

Keywords: cybersecurity, cyberspace, cyberthreat, mathematical models, differential conversion, intelligent techniques, protection of information.