PROCESS MODELING OF MESSAGE DISTRIBUTION IN SOCIAL NETWORKS BASED ON SOCIO-COMMUNICATIVE SOLITONS
Keywords:Social network, graph of message flow, excitation, activity threshold, Cauchy problem, separated wave, soliton, front wave, Boussinesq equation, Korteweg-de Vries equation.
AbstractThe article proposes a new class of models for distributing messages in social networks based on socio- communicative solitons. This class of models allows to take into account the specific mechanisms for transmitting messages in the chains of the network graph, in which each of the vertices are individuals who, receiving a message, initially form their attitude towards it, and then decide on the further transmission of this message, provided that the corresponding potential of the interaction of two individuals exceeds a certain threshold level. The authors developed the original algorithm for calculating the time moments of message distribution in the corresponding chain, which comes to the solution of a series of Cauchy problems for systems of ordinary nonlinear differential equations. A special continualization procedure is formulated, which makes it possible to simplify substantially the resulting system of equations and replace a part of the equations by the Boussinesq or Korteweg-de Vries equations. The presence of soliton solutions to the above-mentioned equations provides grounds for considering socio-communicative solitons as an effective tool for modeling the processes of distributing messages in social networks and investigating the diverse influences on their dissemination processes.
A. Bomba, M. Nazaruk, N. Kunanets, V. Pasichnyk, “Constructing the diffusion-liked model of bicomponent knowledge potential distribution,” International Journal of Computing, vol. 16, Issue 2, pp.74-81, 2017.
D. K. Horkovenko, “Overview of the models of information distribution in social networks,” Young scientist, no. 8, pp. 23-28, 2017. (in Russian).
H. A. Hubanov, D. A. Novikov, A. H. Chshartishvili, Social Networks: Modeling of Information Influence, Management and Confrontation, 2010, 228 p. (in Russian).
H. A. Hubanov, “Review of online reputation / trust systems,” Internet Conference on Governance Issues, 25 p., 2009. (in Russian).
M. Cha, H. Haddadi, F. Benevenuto, K. P. Gummadi, “Measuring user influence in Twitter: the million follower fallacy,” Proceedings of the ICWSM’10, 2010.
M. Goetz, J. Leskovec, M. Mcglohon, C. Faloutsos, “Modeling blog dynamics,” Proceedings of the ICWSM’09, 2009.
J. Leskovec, L. Backstrom, J. Kleinberg, “Meme-tracking and the dynamics of the news cycle,” Proceedings of the KDD’09, 2009.
D. Liben-Nowell, J. Kleinberg, “Tracing information flow on a global scale using Internet chain-letter data,” PNAS, vol. 105, issue 12, pp. 4633–4638, 2008.
M. V. Nosova, L. I. Sennikova, “Modeling the information dissemination in decentralized network systems with irregular structure,” New Information Technologies and Automated Systems, no. 17, pp. 8-15, 2014. (in Russian).
D. J. Daley, D. G. Kendall, “Stochastic rumors,” J. Inst. Math. Appl., vol. 142, pp. 42-55, 1965.
D. Kempe, J. Kleinberg, E. Tardos, “Maximizing the spread of influence through a social network,” Proceedings of the 9-th ACM SIGKDD International Conference on Knowledge Discovery and Data Mining, 2003, pp. 137–146.
R. B. Myerson, Game Theory: Analysis of Conflict, London: Harvard Univ. Press, 1991.
J. Goldenberg, B. Libai, E. Muller, “Talk of the Network: A Complex Systems Look at the Underlying Process of Word-of-Mouth,” Marketing Letters, no. 2, pp. 11-34, 2001.
H. W. Hethcote, “The mathematics of infectious diseases,” SIAM Review, vol. 42, issue 4, pp. 599–653, 2000.
R. Isea, R. Mayo-García, “Mathematical analysis of the spreading of a rumor among different subgroups of spreaders,” Pure and Applied Mathematics Letters, vol. 2015, pp. 50-54, 2015.
S. K. Kuizheva, “About the mathematical tools of the research of social and economic systems,” TERRA ECONOMICUS, vol. 12, no. 2, part 3, pp. 46-51, 2014. (in Russian).
S. K. Kuizheva, “The Korteweg-de Vries equation and mathematical models of social and economic systems,” Bulletin of the Adyghe State University. Series 4: natural-mathematical and technical sciences, no. 154, pp. 20-26, 2015. (in Russian).
S. H. Lomakin, A. M. Phedotov, “Analysis of the model of information distribution in the cellular automata network,” Bulletin of Novosibirsk State University. Series: Information Technology, pp. 86-97, 2014. (in Russian).
V. A. Minaev, A. S. Ovchinskii, S. V. Skryl, S. N. Trostianskii, How to Control Mass Consciousness: Modern Models, Monograph, 2013, 200 p. (in Russian).
E. Rogers, Diffusion of Innovations, 4 ed. N.Y.: Free Press, 1995.
A. Baronchelli, M. Felici, E. Caglioti, V. Loreto, L. Steels, “Evolution of opinions on social networks in the presence of competing committed groups,” J. Stat. Mech. URL: http://arxiv.org/ abs/1112.6414
L. Dallsta, A. Baronchelli, A. Barrat, V. Loreto, “Non-equilibrium dynamics of language games on complex networks,” URL: http://samarcanda.phys.uniroma1.it/vittorioloreto/publications/ language-dynamics/
Q. Lu, G. Korniss, B. K. Szymanski, “Naming games in two-dimensional and small-world-connected random geometric networks,” URL: http://journals.aps.org/pre/abstract/10.1103/PhysRevE.77.016111.
A. Baronchelli, “Role of feedback and broadcasting in the naming game,” Phys. Rev. E., vol. 83, Article 046103, 2011.
A. I. Lobanov, “Models of cellular automata,” Computer Studies and Modeling, no. 3, pp. 273-293, 2010. (in Russian).
M. V. Altaiskii, N. E. Kaputkina, V. A. Krylov, “Quantum neural networks: current state and prospects of development,” Physics of Elementary Particles and the Atomic Nucleus, vol. 45, 43 p., 2014. (in Russian).
A. Cabello et al., “Quantum social networks,” J. Math. Phys. A., vol. 45., pp. 285101, 2012.
F. Beck, “Synaptic quantum tunnelling in brain activity,” Neuroquantology, vol. 6, no. 2, pp. 140-151, 2008.
Yu. E. Elkin, “The simplest models of excitable media”.
A. L. Hodgkin, A. F. Huxley, “A quantative description of membrane current and its application conduction and excitation in nerve,” J. Physiol., no. 117, pp. 500-544, 1952.
R. A. Fitzhugh, “Impulses and physiological states in theoretical model of nerve membrane,” Biophys. J., no. 1, pp. 445-466, 1961.
A. T. Winfree, “Varieties of spiral wave behaviour – an experimentalist's approach to the theory of excitable media,” Chaos, no. 1, pp. 303-334, 1991.
R. R. Aliev, A. V. Panfilov, “Asimple model of cardiac excitation,” Chaos, Solitons &Fractals, vol. 7, no. 3, pp. 293-301, 1996.
E. C. Zeeman, Differential Equations for the Heartbeat and Nerve Impulses, Mathematical Institute, University of Warvick, Coventry, 1972.
V. N. Biktashev, “Dissipation of excitation of wavefronts,” Phys. Rev. Lett., no. 89(16), 2002.
R. Suckley, V. N. Biktashev, “30 years on: a comparison of asymptotics of heart and nerve excitability”.
A. P. Mikhailov, A. P. Petrov, N. A. Marevtseva, I. V. Tretiakova, “Development of the model for the information dissemination in the society of 2014,” Mathematical Modeling, vol. 26, issue 3, pp. 65-74, 2014. (in Russian).
A. P. Mikhailov, K. V. Izmodenova, “About the optimal control of the propagation process of the formation,” Mathematical Modeling, vol. 17, no. 5, pp. 67–76, 2005. (in Russian).
A. P. Mikhailov, N. A. Marevtseva, “Information fight models”, Mathematical Modeling, vol. 23, no. 10, pp. 19-32, 2011. (in Russian).
L. L. Delitsyn, Quantitative Models of the Spread of Innovations in the Field of Information and Telecommunication Technologies, 2009, 106 p. (in Russian).
V. A. Shvedovskyi, P. A. Mykhailova, “Building an interaction model between electorates,” Mathematical Modeling, vol. 20, no. 7, pp. 107-118, 2008. (in Russian).
N. E. Friedkin, “Structural cohesion and equivalence explanations of social homogeneity,” Sociological Methods and Research, no. 12, pp. 235-261, 1984.
P. A. Prudkovskii, “The theory of nonlinear waves,” W06 Waves in Chains.
V. Yu. Novokshenov, Introduction to the Theory of solitons, Izhevsk, Institute for Computer Research, 2002, 96 p. (in Russian).
A. Bomba, Y. Turbal, M. Turbal, “Method for studying the multi-solitone solutions of the Korteveg de-Vries type equations,” Journal of Difference Equation, vol. 2, pp. 1-10, 2015.
Yu. Turbal, “Necessary and sufficient conditions for the existence of solutions of motion equations for anisotropic elastic bodies I, n the form of solitary waves of the -type -solitons,” Problems of Applied Mathematics and Mathematical Modeling, no. 2012, pp. 78-86, 2012. (in Russian).
U.S. House Representatives (115th Congress) Official Twitter User Timelines, https://doi.org/10.7910/DVN/UIVHQR
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