+ 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.
A mathematical model has been developed and a study of the model of personal data protection from network clustering coefficient and data transfer intensity in social networks has been carried out. Dependencies of protection of the system from the size of the system (and from the amount of personal data); information security threats from the network clustering factor. A system of linear equations is obtained, which consists of the equation: rate of change of information flow from social network security and coefficients that reflect the impact of security measures, amount of personal data, leakage rate, change of information protection from network clustering factor, its size, personal data protection. As a result of solving the system of differential equations, mathematical and graphical dependences of the indicator of personal data protection in the social network from different components are obtained. Considering three options for solving the equation near the steady state of the system, we can conclude that, based on the conditions of the ratio of dissipation and natural frequency, the attenuation of the latter to a certain value is carried out periodically, with decaying amplitude, or by exponentially decaying law. A more visual analysis of the system behavior is performed, moving from the differential form of equations to the discrete one and modeling some interval of the system existence. Mathematical and graphical dependences of the system natural frequency, oscillation period, attenuation coefficient are presented. Simulation modeling for values with deviation from the stationary position of the system is carried out. As a result of simulation, it is proved that the social network protection system is nonlinear.
In Ukraine, the right to protection of personal data is a constitutional guarantee, and the protection of personal data is one of the areas in which such a guarantee should be implemented. The subject of our research will not be objects in general, but dynamic systems of information protection in social networks in the mathematical sense of the term. The study developed a linear mathematical model and conducted a survey of the model of protection of personal data from a set of specific network parameters and the intensity of data transmission in social networks. Dependencies are considered: the amount of information flow in the social network from the components of information protection, personal data, and data flow rate; security of the system from the size of the system and from the amount of personal data; information security threats from a set of specific network parameters.A system of linear equations is obtained, which consists of the equation: rate of change of information flow from social network security and coefficients that reflect the impact of security measures, amount of personal data, leakage rate, changes in information protection from a set of specific network parameters, its size, personal data protection As a result of solving the system of differential equations, mathematical and graphical dependences of the indicator of personal data protection in the social network on various components are obtained. Considering three options for solving the equation near the steady-state of the system, we can conclude that, based on the conditions of the ratio of dissipation and natural frequency, the attenuation of the latter to a specific value is carried out periodically, with attenuation: amplitude, or exponentially fading law. A more visual analysis of the system behavior is performed, moving from the differential form of equations to the discrete one and modeling some interval of the system's existence. Mathematical and graphical dependences of the frequency of natural oscillations of the system, the period of oscillations, and the attenuation coefficient are presented. Simulation modeling for values with deviation from the stationary position of the system is performed. As a result of the simulation, it is proved that the social network protection system is nonlinear.
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