ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)
Menu

1
Issue
vol 66 / January, 2023
Article

DOI 10.17586/0021-3454-2016-59-9-729-734

UDC 004.81; 613.86; 159.913

INDICATION OF MENTAL CONTAMINATION IN ULTRAMETRIC STATE SPACE OF p-ADIC MODEL OF THE SUBJECT’S BEHAVIOR

K. O. Gnidko
A. F. Mozhaisky Military Space Academy, Department of Information Collecting and Processing Systems;


R. B. Zholus
A. F. Mozhaisky Military Space Academy;


Read the full article 

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

References:
  1. Gnidko K.O., Lomako A.G. Trudy SPIIRAN (SPIIRAS Proceedings), 2015, no. 38, pp. 9–33. (in Russ.)
  2. Gnidko K.O., Lomako A.G., Zholus R.B. Trudy SPIIRAN (SPIIRAS Proceedings), 2015, no. 39, pp. 193–211. (in Russ.)
  3. Gnidko K.O. Trudy SPIIRAN (SPIIRAS Proceedings), 2016, no. 44, pp. 65–82. (in Russ.)
  4. Wilson T.D., Brekke N. Psychological Bull., 1994, no. 1(116), pp. 117–142.
  5. Larrick R., Morgan J., Nisbett R.E. Psychological Science, 1990, no. 1, pp. 362–370.
  6. Einhorn H.J., Hogarth R.M. Annual Rev. of Psychology, 1981, no. 1(32), pp. 53–88.
  7. Fischhoff B., Slovic P., Lichtenstein S. J. of Experimental Psychology: Human Perception and Performance, 1977, no. 3, pp. 552–564. DOI: 10.1037/0096-1523.3.4.552.
  8. Tversky A., Kahneman D. Judgment under Uncertainty: Heuristics and Biases, NY, Cambridge Univ. Press, 1982, pр. 84–100.
  9. Fong G., Krantz D., Nisbett R.E. Cognitive Psychology, 1986, no. 18, pp. 253–292.
  10. Tegmark M. Chaos Solitons Fractals, 2015, no. 76, pp. 238–270. DOI: 10.1016/j.chaos.2015.03.014.
  11. Khrennikov A.Yu. Modelirovanie protsessov myshleniya v р-adicheskikh sistemakh koordinat (Modeling of Processes of Thinking in p-adic Coordinate Systems), Moscow, 2004. (in Russ.)
  12. De Groot J. Proc. of the Amer. Math. Soc., 1956, no. 5(7), pp. 948–953.
  13. Engelking R. General Topology, Berlin, Heldermann Verlag, 1989, 540 p.
  14. Lemin A.J. Algebra Universalis, 2003, no. 1(50), pp. 35–49.
  15. Beardon A.F. Iteration of rational functions: Complex analytic dynamical systems, Springer Science & Business Media, 2000, no. 132.
  16. Khrennikov A.Y. Non-Archimedean Analysis: Quantum Paradoxes, Dynamical Systems and Biological Models, Dordrecht, Springer Netherlands, 1997, 312 p.
  17. Borevich Z.I., Shafarevich I.R. Teoriya chisel (Number theory), Moscow, 1985, 507 р. (in Russ.)