Математична модель визначення ймовірнісних станів інформаційно-комунікаційної системи в умовах ведення кіберборотьби

Formulation of the problem in general. Science has no substantiated system of indicators and cyber warfare effectiveness evaluation criteria. Mathematical modelling of cyber warfare, as a relatively new and innovative area of the Armed Forces of Ukraine activity, is undoubtedly essential and will allow for a comprehensive investigation of the issue of assessing the effectiveness of its conduct, which has not yet received sufficient attention. Research methods. Methods of formalisation and mathematical modelling were used in this research. By the formalisation method, cyber warfare was represented as a diffusion Markov process, in sense of the stochastic processes theory, as well as a set of typical cyber warfare targets were generalised as an information and communication system by the structural feature (most of cyber warfare targets consists of physical, logical and cyber-persona layers). The method of mathematical modelling was used to develop a mathematical model for determining probabilistic states of an information and communication system in the conditions of cyberwarfare. Analysis of the latest research findings. The latest research results in this area highlight only partial indicators of the separate components of cyber warfare (cyber defence, cyber intelligence, and cyber influence) productivity. Such indicators are usually based on the volume of intercepted, modified or destroyed data (information) and its importance, which, in turn, can only be assessed by experts, which a priori generates subjectivity of the cyber warfare effectiveness assessment. Presenting the main results. The main result of the research is the developed mathematical model for determining probabilistic states of an information and communication system in the conditions of cyberwarfare, based on a mathematical apparatus of the stochastic differential equations theory. An element of scientific novelty. The developed mathematical model, unlike existing ones, allows for obtaining probabilistic parameters of the information and communication system, which function as effective indicators of cyber warfare. Such parameters are the mathematical expectations of the information and communication system probabilities of being in determined states and the dispersions of these probability distributions. Theoretical and practical significance of the article. The theoretical importance of the obtained scientific results is the applied use of the powerful mathematical apparatus of the theory of stochastic differential equations for analytical mathematical modelling of cyberspace actions, which are characterised by uncertainty and randomness. The practical significance of the research results is the possibility of using the mathematical model to determine the probabilistic states of the information and communication system software implementation to predict the course and results of cyber warfare. Conclusion and the perspectives of future research. Therefore, the article highlighted the main provisions of the mathematical model for determining probabilistic states of an information and communication system in the conditions of cyberwarfare. The direction of further research in this area is the search and approximation of representative statistics of cyber warfare, the data from which would be suitable for use as parameters (initial data) of the developed mathematical model.