Features of assessing and forecasting the critical infrastructure facilities level of security with components of the Internet of Things technology based on catastrophe theory methods

The object of the study is a new methodological approach to assessing and predicting the level of protection of complex cyber-physical objects, as well as to the construction and application of models and methods of catastro-phe theory, as a new mathematical and methodological tool for increasing the reliability of the assessment and forecast of the level of protection of critical infrastructure objects (CIO) using the Internet of Things technology (ITT) in the interests of timely warning of danger and taking preventive measures to improve their information security. The proposed approach is based on well-known methods of catastrophe theory, in particular, on the methods of studying bifurcations that allow implementing the assessment and forecasting of the level of protection of objects of this class using algorithms for identifying and verifying the boundary and potentially catastrophic state (level) of protection with smoothly increasing changes in the parameters of external conditions, for example, smooth changes in the intensity of detected signs of computer attacks. In this case, the algorithm for assessing and predicting the security level, from the point of view of the mathematics of catastrophe theory and the theory of state spaces, is considered as an analysis of the process of transition of the security level of a critical infrastructure object from state to state. A detailed analysis of the distinctive features of this approach is made, determining the feasibility and conditions of its application for assessing and predicting a potentially dangerous, alarming level of security of CIO using ITT. A sequence of calculations and analytical expressions for calculating the estimated values of the security state (level) for various categories of signs of potential computer attacks are developed and described in detail. The results of experimental calculations are given for an example of assessing and predicting the security state (level) taking into account the intensity of receipt (detection) of various signs of computer attacks on CIO using ITT.