MODELING CONFLICT IN A SOCIAL SYSTEM USING DIFFUSION EQUATIONS
Cite this article as:
Петухов А. Ю., Мальханов А. О., Сандалов В. М., Петухов Ю. В. MODELING CONFLICT IN A SOCIAL SYSTEM USING DIFFUSION EQUATIONS. Izvestiya VUZ. Applied Nonlinear Dynamics, 2016, vol. 24, iss. 6, pp. 65-83. DOI: https://doi.org/10.18500/0869-6632-2016-24-6-65-83
The issue of modeling various kinds of social conflicts using diffusion equations is discussed. The main approaches to and methods of mathematical modeling in contemporary humanitarian sciences. The main concepts of social conflicts, ways of their classification, interpretation, including ethnic-social, religious and other conflicts are considered. The notion of a conflict in a social system is defined in terms of mathematical modeling. A model based on Langevin diffusion equation is introduced. The model is based on the idea that all individuals in a society interact by means of a communication field h. This field is induced by each individual in the society, modeling informational interaction between individuals. An analytical solution of the system of thus obtained equations in the first approximation for a diverging type of diffusion is given. It is shown that even analyzing a simple example of the interaction of two groups of individuals the developed model makes it possible to discover characteristic laws of a conflict in a social system, to determine the effect of social distance in a society on the conditions of generation of such processes, accounting for external effects or a random factor. Based on the analysis of the phase portraits obtained by modeling, it is concluded that there exists a stability region within which the social system is stable and non-conflictive.
DOI: 10.18500/0869-6632-2016-24-6-65-83
Paper reference: Petukhov A.Y., Мalhanov A.О., Sandalov V.М., Petukhov Yu.V. Modeling conflict in a social system using diffusion equations. Izvestiya VUZ. Applied Nonlinear Dynamics. 2016. Vol. 24. Issue 6. P. 65–83.
1. Petukhov А.Y. The Concept of Social Conflict: A Social-energy approach // Vector of Science TSU. 2015. Issue 3–2 (33-2). С. 240–245 (in Russian).
2. Coser L.А. Functions of Social Conflict / Transl. From Engl. By О. Nazarova; Under Edit. L.G. Ionin. Moscow: Idea-Press, House of Intellectual Book, 2000. P. 340 (in Russian).
3. Darendorf R. Elements of the Theory of Social Conflict // Socis (Sociological Studies). 1994. Issue 5. P. 142–147 (in Russian).
4. Boulding К. General Theory of Systems – The Skeleton of Science Studies on the General Theory of Systems. М.: Nauka, 1969. P. 171–182 (in Russian).
5. Davydov S.А. Sociology. Summary of the Lectures. М.: Eksmo, 2008. 160 p. (in Russian).
6. Perov Y.V. Monitoring social conflictogenity of society National Security // Nota Bene. 2014. Issue 4. P. 574–583 (in Russian).
7. Kravchenko А.I. Sociology of Deviantness. М.: MSU, 2003. 727 p. (in Russian).
8. Malkov V.P. Mathematical Modeling of Historical Dynamics: Approaches and Models. M., 2009 (in Russian).
9. Shabrov О.F. A system approach and computer modeling in political science research // Social Sciences and Contemporaneity. 1996. Issue 2. P. 100–110 (in Russian).
10. Mason J.W.D. Consciousness and the structuring property of typical data // Complexity. 2013. Vol. 18, Issue 3. P. 28–37, January/February. DOI: 10.1002/cplx.21431
11. Blauberg I.V., Yudin E.G. Establishing and Essence of the System Approach. М., 1973. P. 301 (in Russian).
12. Saati Т.L., Kerns К.К. Analytical Planning: Organization of Systems. М., 1991. P. 259 (in Russian).
13. Lincoln P. Bloomfield Managing International Conflict. From Theory to Policy: A Teaching Tool Using CASCON. N.Y., 1997. P. 234.
14. Plotnitskiy Yu.М. Models of Social Processes: Textbook for Higher Education Institutions. М., Logos, 2001 (in Russian).
15. Malkov S.Yu. Mathematical Modeling of Historical Dynamics. Approaches and Processes. Edit. М. G. Dmitriyev. М.: RGSU, 2004 (in Russian).
16. Ebeding V. Formation of Structures under Irreversible Processes. Introduction into the Theory of Dissipative Structures. М.: Mir, 1979 (in Russian).
17. Anatomy of Crisis. М.: Nauka, 2000 (in Russian).
18. Romanovskiy Yu.М., Stepanova N.V., Chernavskiy D.S. Mathematical Biophysics. М.: Nauka, 1984 (in Russian).
19. Melik-Gaykazyan I.V. Informational Processes and Reality. М.: Nauka, Fizmatlit, 1998 (in Russian).
20. Haken H. Synergetics. Hierarchy of Instabilities in Self-Organizing Systems and Devices. М.: Mir, 1985 (in Russian).
21. Self-Organization in Non-Equilibrium Systems. М.: Mir, 1979 (in Russian).
22. Nilolis G., Prigozhin I. Cognition of the Complex. М.: Мir, 1990 (in Russian).
23. Malinetskiy G.G., Potapov А.B. Contemporary problems of Nonlinear Dynamics. М.: Editorial URSS, 2000 (in Russian).
24. Malinetskiy G.G. Chaos, Structures, Computation Experiment. Introduction into Nonlinear Dynamics. М.: Nauka, 1997 (in Russian).
25. Loskutov А.Yu., Mikhailov А.S. Introduction into Synergetics. М.: Nauka, 1990 (in Russian).
26. Dmitriyev А.S., Starkov S.О., Shirokov М.Е. Synchronization of ensembles of couples mappings // Izvestiya Vuzov. Applied Nonlinear Dynamics. 1996. Vol. 4, Issue 4–5. P. 40 (in Russian).
27. The New in Synergetics. Mysteries of the World of Non-Equilibrium Systems. М.: Nauka, 1996 (in Russian).
28. Alekseyev Yu.К., Sukhorukov А.P. Introduction into the Catastrophe Theory. М.: MSU Publishers, 2000 (in Russian).
29. Poston Т., Stewart I. The Catastrophe Theory and its Applications. М.: Mir, 1980 (in Russian).
30. Controlling Risk: Risk. Stable development. Synergetics. М.: Nauka, 2000 (in Russian).
31. Holyst J.A., Kacperski K., Schweitzer F. Phase transitions in social impact models of opinion formation // Physica. 2000. Vol. A285. P. 199–210.
32. Mikhailov А.P. Modeling the «Power–Society» System. Nizhniy Tagil: State Soc.-Ped. Academy [et al.]. Nizhniy Tagil, 2006 (in Russian).
33. Mikhailov А.P. Gorbatikov Е.А. A basic model of the duumvirate in the «Power-Society» system // Mathematical Modeling. 2012. Vol. 24, Issue 1. P. 33–45 (in Russian).
34. Mikhailov А.P., Petrov А.P. Behavioristic hypotheses and mathematical modeling in humanitarian sciences // Math. Modeling. 2011. Vol. 23, Issue 6. P. 18–32 (in Russian).
35. Bonabeau E. Agent-based modeling: A revolution? // Proc. National Academy of Sciences 99, Suppl. 3: 2002. 7199-200.
36. Casti J. Agent-based modeling: Methods and techniques for simulating human systems. Proc. National Academy of Sciences 99: 7280-7, 1997.
37. Wiley Gilbert N., Troitzsch K.G. Would-Be Worlds: How Simulation Is Changing the World of Science. New York, 1999.
38. Charles M., North M. Simulation for the Social Scientist. Tutorial on Agent-based Modeling and Simulation // Buckingham: Open University Press, Proc. 2005. Winter Simulation Conference, Orlando, FL, Dec. 2005, 4–7. P. 2–15. Available at http://www.informssim.org/wsc05papers/002.pdf.
39. Charles M., North. M. Tutorial on Agent-based Modeling and Simulation. Part 2: How to Model with Agents // Proc. 2006 Winter Simulation Conference, L.F. Perrone, F.P. Wieland, J. Liu, B.G. Lawson, D.M. Nicol, and R.M. Fujimoto, eds., Monterey, CA, Dec 2006, 3–6.
40. Prietula M.J., Carley K.M., Gasser L., eds. Simulating Organizations: Computational Models of Institutions and Groups. Cambridge, MA: MIT Press, 1998.
41. Gutz А.К., Коrobitsyn V.V. et al. Mathematical Models of Social Systems Textbook. Omsk: Omsk State University, 2000 (in Russian).
42. Petukhov А.Y. Modeling Social and Political Processes in the Conditions of Informational Wars // Social-Energy Approach Fractal Simulation. 2012. Vol. 3, Issue 1. P. 16–32 (in Russian).
43. Petukhov A.Y. Modeling of branched chain reactions in political and social processes //Global Journal of Pure and Applied Mathematics. 2015. Vol. 11, Issue 5. P. 3401– 3408.
44. Petukhov A.Y., Polevaya S.A., Yakhno V.G. The theory of information images: Modeling based on diffusion equations // Int. J. Biomath. 2016. 09. 1650087. DOI: http:dx.doi.org/10.1142/S179352451650087X
45. Ermolaev O. Mathematical Statistics for Psychologists. M.: SAG, Flinta, 2002. 325 p. (in Russian).
46. Heritage A.D. Mathematical Methods in Psychological Research. Analysis and Interpretation of Data. SPb: Rech, 2004. (in Russian).
47. Andronov А.А., Vitt А.А., Haykin S.E. The Theory of Oscillations. 2-nd edition, revised and corrected. М.: Nauka, 1981. 918 p. (in Russian).
48. Goryachenko V.D. Elements of the Theory of Oscillations: Textbook. 2-nd edition, revised and added. М.: Higher School, 2001. 395 p. (in Russian).
BibTeX
author = {Alexandr Y. Petukhov and Alexey О. Мalhanov and Vladimir М. Sandalov and Yury V. Petukhov},
title = {MODELING CONFLICT IN A SOCIAL SYSTEM USING DIFFUSION EQUATIONS},
year = {2016},
journal = {Izvestiya VUZ. Applied Nonlinear Dynamics},
volume = {24},number = {6},
url = {https://old-andjournal.sgu.ru/en/articles/modeling-conflict-in-social-system-using-diffusion-equations},
address = {Саратов},
language = {russian},
doi = {10.18500/0869-6632-2016-24-6-65-83},pages = {65--83},issn = {0869-6632},
keywords = {Social conflict,society,diffusion equations,Langevin equation,communication field.},
abstract = {The issue of modeling various kinds of social conflicts using diffusion equations is discussed. The main approaches to and methods of mathematical modeling in contemporary humanitarian sciences. The main concepts of social conflicts, ways of their classification, interpretation, including ethnic-social, religious and other conflicts are considered. The notion of a conflict in a social system is defined in terms of mathematical modeling. A model based on Langevin diffusion equation is introduced. The model is based on the idea that all individuals in a society interact by means of a communication field h. This field is induced by each individual in the society, modeling informational interaction between individuals. An analytical solution of the system of thus obtained equations in the first approximation for a diverging type of diffusion is given. It is shown that even analyzing a simple example of the interaction of two groups of individuals the developed model makes it possible to discover characteristic laws of a conflict in a social system, to determine the effect of social distance in a society on the conditions of generation of such processes, accounting for external effects or a random factor. Based on the analysis of the phase portraits obtained by modeling, it is concluded that there exists a stability region within which the social system is stable and non-conflictive. DOI: 10.18500/0869-6632-2016-24-6-65-83 Paper reference: Petukhov A.Y., Мalhanov A.О., Sandalov V.М., Petukhov Yu.V. Modeling conflict in a social system using diffusion equations. Izvestiya VUZ. Applied Nonlinear Dynamics. 2016. Vol. 24. Issue 6. P. 65–83. Download full version }}