Geodesic
Modified Krasnoshchekov model in case of the reducible matrix of social interactions
Matematičeskoe modelirovanie, Tome 29 (2017) no. 12, pp. 3-15.

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In this paper Krasnoshchekov’s model, describing the behavior of people in the community under social and informational influences, is extended in the case of the system, having the sophisticated structure of social interactions. In particular, the situation in which is formed an isolated group of people, unfamiliar with the rest of the community, which corresponds to the decomposability of the matrix of social interactions is under consideration. Conditions of the existence and uniqueness solution of the equations, describing the behavior of such a community are investigated. The problem of the connection between Krasnoshchekov’s and De Groot’s model is fixed. The way, how the above matrix and social independence of individuals affect on the solution of this system structure, which describes, in particular, the spread of beliefs among the people is also investigated.
Keywords: conformity, decision-making, reducible matrices, social graphs, belief systems, superconductivity.
Mots-clés : productive matrices, stochastic matrices 
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I. V. Kozitsin. Modified Krasnoshchekov model in case of the reducible matrix of social interactions. Matematičeskoe modelirovanie, Tome 29 (2017) no. 12, pp. 3-15. http://geodesic.mathdoc.fr/item/MM_2017_29_12_a0/

[1] G.V. Grachev, I.K. Melnik, Manipulirovanie lichnostiu: organizatsiia, sposoby i tekhnologii informatsionno-psikhologicheskogo vozdeistviia, IF RAN, M., 1999

[2] J.C. Turner, Social influence, Thomson Brooks / Cole Publishing Co, 1991

[3] D.A. Gubanov, D.A. Novikov, A.G. Chkhartishvili, Socialnye seti: modeli informatsionnogo vliianiia, upravleniia i protiviborstva, Fizmatlit, M., 2010, 228 pp.

[4] D.A. Gubanov, D.A. Novikov, A.G. Chkhartishvili, “Modeli vliianiia v sotsialnykh setiakh (obzor)”, Upravlenie bolshimi sistemami, 27 (2009), 205–281

[5] D.A. Gubanov, D.A. Novikov, A.G. Chkhartishvili, “Modeli informatsionnogo vliianiia i informatsionnogo upravleniia v sotsialnykh setiakh”, Problemi upravleniia, 2009, no. 5, 28–35

[6] A.M. Raigorodskii, Modeli interneta, Izdatelskii dom “Intellekt”, Dolgoprudnii, 2013

[7] E. Bonson, S. Royo, M. Ratkai, “Citizens' engagement on local governments' Facebook sites. An empirical analysis: The impact of different media and content types in Western Europe”, Government Information Quarterly, 32:1 (2015), 52–62 | DOI

[8] K. Peters, Y. Chen, A.M. Kaplan, B. Ognibeni, K. Pauwels, “Social media metrics – A framework and guidelines for managing social media”, Journal of interactive marketing, 27:4 (2013), 281–298 | DOI

[9] R.M. Bond et al., “A 61-million-person experiment in social influence and political mobilization”, Nature, 489:7415 (2012), 295–298 | DOI

[10] S. Boulianne, “Social media use and participation: A meta-analysis of current research”, Information, Communication Society, 18:5 (2015), 524–538 | DOI

[11] S. Stieglitz, L. Dang-Xuan, “Social media and political communication: a social media analytics framework”, Social Network Analysis and Mining, 3:4 (2013), 1277–1291 | DOI

[12] P. Sobkowicz, M. Kaschesky, G. Bouchard, “Opinion mining in social media: Modeling, simulating, and forecasting political opinions in the web”, Government Information Quarterly, 29:4 (2012), 470–479 | DOI

[13] M.H. DeGroot, “Reaching a consensus”, Journal of the American Statistical Association, 69:345 (1974), 118–121 | DOI | Zbl

[14] N.E. Friedkin, E.C. Johnsen, “Social influence networks and opinion change”, Advances in group processes, 16:1 (1999), 1–29 | MR

[15] P.S. Krasnoshchekov, “The simplest mathematical model of behaviour. Psychology of conformism”, Matematicheskoe Modelirovanie, 10:7 (1998), 76–92

[16] S.E. Asch, “Studies of independence and conformity: I. A minority of one against a unanimous majority”, Psychological monographs: General and applied, 70:9 (1956), 1 | DOI

[17] D. Kempe, J. Kleinberg, E. Tardos, “Maximizing the spread of influence through a social network”, Proceedings of the ninth ACM SIGKDD international conference on Knowledge discovery and data mining, ACM, 2003, 137–146 | DOI | MR

[18] D.J. Watts, P.S. Dodds, “Influentials, networks, and public opinion formation”, Journal of consumer research, 34:4 (2007), 441–458 | DOI | MR

[19] F.R. Gantmacher, Matrix theory, v. 1, 2, Chelsea, New York, 1959 | MR

[20] S. A. Ashmanov, Vvedenie v matematicheskuiu ekonomiku, Nauka, M., 1984, 296 pp.

[21] F. Harary et al., Graph theory, 1969

[22] A.A. Belolipetskii, I.V. Kozitsin, “Dynamic variant of mathematical model of collective behavior”, Journal of Computer and Systems Sciences International, 56:3 (2017), 385–396 | DOI

[23] C. Castellano, S. Fortunato, V. Loreto, “Statistical physics of social dynamics”, Reviews of modern physics, 81:2 (2009), 591 | DOI