The Information Security Management System is an important element in preventing possible threats and failures, exposure to various internal and external factors, which could lead to irreversible consequences. Predicting the impact of various types of incidents allows to ensure the stability and balance of complex dynamic systems, their confidentiality, integrity and availability. The resilience of the information security management system to different types of cyber incidents has been researched. Mathematical Catastrophe theory has been applied to model the dynamics of the information system. Different types of catastrophes that depend on the number of influencing parameters on the dynamic system were analyzed and investigated. The main types of incidents for research have been identified based on the report of detected cyber incidents in the period 2022–2024. It was analyzed the list of categories of cyber incidents, which is constantly updated taking into account the appearance of new types, and also includes a description of these incidents and their impact on the information system. The “Butterfly” type of catastrophe has been chosen to simulate the behavior of dynamic system
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