Abstract
The improvement of protection systems is based on the introduction and use of a mathematical apparatus. Ensuring the confidentiality, integrity and availability of information is an urgent and important problem in the modern world. Crisis processes are characteristic phenomena in security systems, so stochastic models cannot always describe their functioning and give a solution. An effective tool for solving this problem can be the use of dynamic models based on the provisions of catastrophe theory. This study is devoted to the analysis of modern approaches to the use of the basic provisions of catastrophe theory in cybersecurity systems. The work presents a brief historical view of the development of this theory and highlights the main definitions: bifurcations, attractors, catastrophes. Elementary catastrophes, their forms and features are characterized. A review of the literary sources of the use of catastrophe theory in information and cyber security was carried out. The analysis made it possible to single out that this theory has not yet been widely implemented, but there are point scientific developments in the process of detecting network anomalies in the cloud environment. The considered approaches to the application of catastrophe theory in information and cyber security can be used to train specialists in the specialty 125 Cybersecurity in the process of research
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