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+ Linear and dynamic models of the system of information security in social networks, taking into consideration the relationships between users, were studied and the resistance of the security system was analyzed. There is a practical interest in studying dependence of the behavior of the system of social network security on the parameters of users’ interaction. Dynamic systems of information security in social networks in the mathematical sense of this term were considered. A dynamic system refers to any object or process, for which the concept of state as a totality of certain magnitudes at a given time is unambiguously defined and the law that describes a change (evolution) of the initial state over time was assigned. The network of social interactions consists of a totality of social users and a totality of the relations between them. Individuals, social groups, organizations, cities, countries can act as users. Relations imply not only communication interactions between users but also relations of the exchange of various resources and activities, including conflict relations. As a result of research, it was found that the security systems of a social network are nonlinear. Theoretical study of the dynamic behavior of an actual object requires the creation of its mathematical model. The procedure for developing a model is to compile mathematical equations based on physical laws. These laws are stated in the language of differential equations. Phase portraits of the data security system in the MATLAB/Multisim program, which indicate the stability of a security system in the working range of parameters even at the maximum value of the impacts, were determined. Thus, the influence of users’ interaction parameters on the parameters of the system of social network security was explored. Such study is useful and important in terms of information security in the network, since the parameters of users’ interaction significantly affect, up to 100 %, the security indicator.

The analysis of parameters of social networks (information transfer to other users, traffic density, probability of network construction) is carried out.  Three variants of solving the equation near the steady state of the system are considered.  The protection of personal data increases from the growing factors of trust in information.Mathematical modeling of the dependence of personal data protection on trust is performed. The results obtained in the article showed that the protection of personal data is directly proportional to the reliability and trust, with constant security parameters.  The protection of personal data increases with the growth of trust parameters.

The article proposes an approach to increase the efficiency of vulnerability validation during automatic active analysis of security of corporate networks based on control of the sequence of implementation of offensive actions (exploits) according to softmax action selection strategy using Gibbs probability distribution. At the same time, based on a practical analysis of the process of validation of vulnerabilities, the coefficient of erroneous decisions on the implementation of the exploit was introduced, which allows to dynamically change the key parameter of the Gibbs distribution - temperature, which in turn balances the probability of choosing the next attack. when implementing the validation of the identified vulnerabilities of a specific target system.

The subject of the article is the models of protection of official, commercial, confidential and other information, which is used by the officials of enterprises when making managerial decisions in terms of destabilizing informative influences. The aim of the study is to obtain an integral index, which characterizes the protection of necessary information, which is used by the officials of the enterprise when making managerial decisions in the presence of destabilizing information influences from the social networks, open sources and insiders. The task of this work are determinations of basic parameters, that characterize the system of defense of information of enterprise at the acceptance of administrative decisions a public servant in the conditions of destabilizing informative influences. The methods of researches are a probability theory and quality theory of differential equalizations. Results: on the basis of the observation and research of the activity of officials in the enterprises of different forms of ownership it was established that making managerial decisions by an official of the enterprise under conditions of destabilizing information influence is a relaxation fluctuation in the non-autonomous model of psychological arousal. An analysis of the dynamics of the sequence of influencing impulses on an official from existing information sources was conducted. An integral index, that determines a thresholding at that the system of informative defense of enterprise answers politicians of informative defense of enterprise at the acceptance of administrative decisions, is got. Conclusions: it was found that the threat of successful destabilizing information influence on management decision making by an official of the enterprise is determined by three parameters: the parameter, which determines the leakage of confidential information, the parameter, which determines the violation of the integrity of information and the parameter, which determines the blocking of access to information. It is noticed that the beginning of the emergence of a sequence of influencing destabilizing information influences on the enterprise determined by the content of the information at the initial moment of time (the effect of suggestion) and occurs over a period of time (lag effect).

У роботі запропоновано підхід отримання миттєвого розрахунку ймовірностей негативних наслідків від успішної реалізації кібератак на об'єкти інформаційної діяльності на основі теорії диференціальних рівнянь із запізненням і механізму побудови логічної Fuzzy -функції. Це дає можливість здійснювати діагностику стану захищеності інформаційної системи.Ключові слова: кіберзахист, fuzzy-функція,інтенсивність кібератак,функція належності, щільність розподілу ймовірності.