Abstract. The problem of ensuring information and psychological security is considered. A universal approach to proactively respond to potentially dangerous conditions of individual and group consciousness, based on mathematical modeling and forecasting of dynamics of mental state of a thinking system in ultrametric p-adic coordinate system is proposed. Application of the lattice theory to ultrametric modelling of mental dynamics is justified. A hypothesis concerning possibility of formal mathematical description of mental contamination as a subset in phase space of dynamic behavior model of a person is formulated and substantiated. Statements and appropriate proofs regarding the number and properties of fixed points of monomial dynamic systems as well as objects generated by them – attractors, repellers, and Siegel disks are presented. An essential theoretical contribution made to the theory of identification consists in application of abstract non-Archimedean analysis to modelling of states dynamics of conscience as specific complex system.

Keywords: proactive security, mental contamination, information and psychological security, risk prevention, p-adic computation, non-Archimedean analysis, identification theory

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