Modeling group behavior based on stochastic cellular automata with memory and systems of differential kinetic equations with delay
The article describes a complex of microkinetic (based on cellular automata) and macrokinetic (based on systems of kinetic differential equations) models describing the group behavior of users in complex social systems. To assess the values of the parameters of the complex of models and use them to simulate the group behavior of voters, the sociological data of the electoral campaign of 2015-2016, selected by the US president, were processed using the method of almost periodic functions. With the help of the developed models, in particular, for example, electoral processes can be simulated, during which the choice of preferences from several possible ones is carried out. For example, with two candidates, the choice is made of three states: for candidate A, for candidate B and the undecided (candidate C). The dynamics of change in preferences of voters are described graphically by a diagram of possible transitions between states, on the basis of which one can obtain a system of differential kinetic equations describing the specified process. In the developed model of stochastic cellular automata with variable memory, at each step of the process of interaction between its cells, a new network of random connections is established, the minimum and maximum number of which is chosen from the specified range. At the initial time, each type of cell is assigned a numeric parameter that specifies the number of steps during which it will retain its type (cell memory). The transition of cells between states is determined by the total number of cells of different types with which there was interaction at a given number of memory steps. After a number of steps equal to the depth of the memory, it passes to the type that had the maximum value of its sum. The effect of external factors (eg, media) on changes in node types, for each step, can be specified using the transition probability matrix. The conducted studies show a good agreement between the data observed in sociology and theoretical calculations.
Keywords
групповое поведение,
диаграммы переходов,
стохастические клеточные автоматы,
кинетические дифференциальные уравнения,
group behavior,
conversion charts,
stochastic cellular automata,
kinetic differential equationsAuthors
| Istratov Leonid Andreevich | Russian Technological University | kuyahshtibov@gmail.com |
| Smichkova Anna Gulamovna | Russian Technological University | nsmych@yandex.com |
| Zhukov Dmitry Olegovich | Russian Technological University | zhukovdm@ya.ru |
Всего: 3
References
Bonica A., Rosenthal H.B., Rothman D.J.C. The political polarization of physicians in the United States: an analysis of campaign contributions to federal elections, 1991 through 2012 // JAMA Internal Medicine. 2014. V. 174, is. 8. P. 1308-1317.
Panagopoulos C. The dynamics of voter preferences in the 2010 congressional midterm elections // Forum. 2010. V. 8, is. 4. Article 9.
Mundim P.S. The press and the vote in the 2002 and 2006 Brazilian presidential campaigns // Revista de Sociologia e Politica, 2012. V. 20, is. 41. P. 123-147.
Dassonneville R. Electoral volatility, political sophistication, trust and efficacy: a study on changes in voter preferences during the Belgian regional elections of 2009 // Acta Politica. 2012. V. 47, is. 1. P. 18-41.
Dewan T.A., Shepsle K.A.B. Political economy models of elections // Annual Review of Political Science. 2011. V. 14. P. 311-330.
Gormley I.C., Murphy T.B. A grade of membership model for rank data // Bayesian Analysis. 2009. V. 4, is. 2. P. 265-296.
Gasser L. social conceptions of knowledge and action: DAI foundations and open system semantics // Artificial Intelligence. 1991. V. 47, No. 1-3. P. 107-138.
Jennings N.R., Faratin P., Lomuscio A.R., Parsons S., Sierra C., Wooldridge M. Automated negotiation: prospects, methods and challenges // International Journal of Group Decision and Negotiation. 2001. V. 10, No. 2. Р. 199-215.
Plikynas D., Raudys A., Raudys S. Agent-based modelling of excitation propagation in social media groups // J. of Experimental and Theoretical Artificial Intelligence. 2015. V. 27 (4). P. 1-16.
Easley D., Kleinberg J. Networks, Crowds, and Markets: Reasoning about a highly connected world. Cambridge : Cambridge University Press, 2010.
Karsai M., In~iguez G., Kaski K., Kert'esz J. Complex contagion process in spreading of online innovation // J. R. Soc. Interface. 2014. V. 11. 20140694.
Centola D., Macy M. Complex contagions and the weakness of long ties // Am. J. Sociol. 2007. V. 113. P. 702-734.
Barrat A., Barth'elemy M., Vespignani A. Dynamical processes on complex networks. Cambridge : Cambridge University Press, 2008.
Watts D.J. A simple model of global cascades on random networks // Proc. Natl. Acad. Sci. USA. 2002. V. 99. P. 5766-5771.
Gleeson J.P., Cahalane D.J. Seed size strongly affects cascades on random networks // Phys. Rev. E. 2007. V. 75. 056103.
Granovetter M., Soong R. Threshold models of diffusion and collective behavior // J. Math. Sociol. 1983. V. 9. P. 165-179.
Gleeson J.P. Binary-state dynamics on complex networks: Pair approximation and beyond // Phys. Rev. X. 2013. V. 3. 021004.
Gleeson J.P. High-accuracy approximation of binary-state dynamics on networks // Phys. Rev. Lett. 2012. V. 107. 068701.
Ya'gan O., Gligor V. Analysis of complex contagions in random multiplex networks // Phys. Rev. E. 2012. V. 86. 036103.
Nematzadeh A., Ferrara E., Flammini A., Ahn Y.-Y. Optimal network modularity for information diffusion // Phys. Rev. Lett. 2014. V. 113. 088701.
Singh P., Sreenivasan S., Szymanski B.K., Korniss G. Threshold-limited spreading in social networks with multiple initiators // Sci. Rep. 2013. V. 3. 2330.
Piedrah'ita P., Borge-Holthoefer J., Moreno Y., Arenas A. Modeling self-sustained activity cascades in socio-technical networks // Europhys. Lett. 2013. V. 104. 48004.
Kocsis G., Kun F. Competition of information channels in the spreading of innovations // Phys. Rev. E. 2011. V. 84. 026111.
Airoldi E.M., Blei D.M., Fienberg S.E., Xing E.P. Mixed membership stochastic blockmodels // J. Mach. Learn. Res. 2008. V. 9. P. 1981-2014.
Zhukov D., Khvatova T., Zaltsman A. Stochastic Dynamics of Influence Expansion in Social Networks and Managing Users' Transitions from One State to Another // Proc. of the 11th European Conf. on Information Systems Management (ECISM). 2017. P. 322-329.
Khvatova T.Yu., Zaltsman A.D., Zhukov D.O. Information processes in social networks: Percolation and stochastic dynamics. CEUR // Workshop Proc. 2nd Int. Scientific Conf. "Convergent Cognitive Information Technologies", Convergent 2017. V. 2064. P. 277-288.
Khvatova T., Block M., Zhukov D., Lesko S. How to measure trust: the percolation model applied to intra-organisational knowledge sharing networks // J. of Knowledge Management. 2016. V. 20, is. 5. P. 918-935.
Zhukov D., Khvatova T., Lesko S., Zaltsman A. Managing social networks: applying Percolation theory methodology to understand individuals' attitudes and moods // Technological Forecasting and Social Change. 2018. V. 129. P. 297-307.
Hay J., Flynn D. How external environment and internal structure change the behavior of discrete systems // Complex Systems. 2016. V. 25 (1). P. 39-49.
Hay J., Flynn D. The effect of network structure on individual behavior // Complex Systems. 2014. V. 23 (4). P. 295-311.
Wang A., Wu W., Chen J. Social network rumors spread model based on cellular automata // Proc. 2014 10th Int. Conf. on Mobile Ad-Hoc and Sensor Networks. MSN. 2014.
Li J., Chen Z., Qin T. Document Using cellular automata to model evolutionary dynamics of social network // IET Conference Publications (644 CP). 2013. P. 200-205.
Левитан Б.М. Почти-периодические функции. М. : Гостехиздат, 1953.
