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Volodymyr Akhramovich

Abstract: 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.
Keywords: modeling / personal data / coefficient / social network / differential / equations / behavior / protection

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