A Discrete Dynamic Conflict Model

Relevance. Conflicts play a significant role in the development of society, the state and all of humanity. They arise in interpersonal relationships, economics, organizational activities, social problems, and world politics. The study of the essence of conflicts, the causes of their emergence and ways to resolve them is carried out by conflictology, which was formed as an interdisciplinary field of knowledge in the middle of the 20^th century. Currently, it has become obvious that the conflict itself is not a negative phenomenon, but a competently resolved conflict situation can benefit all parties to the conflict. As a result, it became necessary to consider conflicts not only from a descriptive, philosophical point of view, but also to be able to predict a possible conflict situation, describe its development over time and calculate acceptable ways out of it. This approach to the study of conflicts is mathematical modeling, based on mathematical methods for describing conflict situations, which allow analyzing conflicts and predicting their outcome.

The purpose is to describe a general methodology for constructing a conflict scheme of any origin within the framework of the mathematical theory of conflicts. The objectives is to consider and analyze a discrete dynamic model of conflicts using the example of a childparent conflict.

Methodology. The work uses algebraic methods and methods of discrete mathematics.

Results. Within the framework of the mathematical theory of conflicts, a conflict with a discrete mismatch is considered the example of a child-parent model conflict. A general method for constructing a conflict situation diagram and analyzing it has been developed. Possible ways of influencing the conflicting parties on each other in any conflict situation are discussed. When analyzing possible scenarios for the development of a conflict situation, the possible types of impacts of the conflicting parties on each other are considered.

Conclusions. Based on the developed dynamic discrete model, it is shown that the mathematical description of conflicts is reduced to the problem of combinatorial optimization. The developed scheme of mathematical description of conflicts can be applied to a wide class of conflict situations in various subject areas.

1. Fadeev A. S., Nichipor V. I. Voennye konflikty sovremennosti, perspektivy razvitiya sposobov ikh vedeniya. Pryamye i nepryamye deistviya v vooruzhennykh konfliktakh XXI veka [Military Conflicts of Modernity, Prospects for the Development of Methods of Their Conduct. Direct and indirect actions in armed conflicts of the twenty-first century]. Voennaya mysl' = Military Thought, 2019, no. 9, pp. 33‒41.

2. Tomin L. V. Sotsial'no-ekonomicheskie konflikty v ramkakh "kapitalizma platform" [SocioEconomic Conflicts in the Framework of "Platform Capitalism"]. Konfliktologiya = Conflictology, 2019, no. 14(3), p. 33.

3. Kilmashkina T. Konfliktologiya. Sotsial'nye konflikty [Conflictology. Social conflicts]. 2nd ed. Moscow, GONITI ‒ DANA, Zakon i pravo,' Publ., 2017. 287 p.

4. Rogochaya G. P. [Religious Conflicts in the Modern World: Approaches to Research]. Pivovarovskie chteniya. Sinteticheskaya paradigma: nauka, filosofiya, religiovedenie: sbornik materialov konferentsii [Pivovar's Readings. Synthetic Paradigm: Science, Philosophy, Religious Studies]. Ekaterinburg, Delovaya kniga Publ., 2019, pp. 264‒266. (In Russ.)

5. Bitkeeva A. N., Kirilenko S. V. Yazykovye konflikty [Language conflicts]. Sotsiolingvistika = Sociolinguistics, 2022, no. 4 (12), pp. 199‒208.

6. Bülow A., eds. Parent–adolescent interaction quality and adolescent affect—An experience sampling study on effect heterogeneity. Child Development, 2022, no. 93(3), pp. 315‒331.

7. Jingyi Xu, Yao Zheng. Parent- and Child-Driven Daily Family Stress Processes between Daily Stress. Parental Warmth, and Adolescent Adjustment. Journal of Youth and Adolescence, 2022, no. 52(3), pp. 490‒505. https://doi.org/10.1007/s10964-022-01691-5

8. Antsupov A. Y., Shipilov A. I. Konfliktologiya [Conflictology]. Moscow, UNITY Publ., 2000. 551 p.

9. Vinyamata E. Conflictology: A multidisciplinary vision. J. Confl, 2010, no. 1(1), p. 1.

10. Clardy A. Managing Organizational Conflict: Towards a Comprehensive Framework of Outcomes, Practices, and Competencies. Perform. Improv, 2018, no. 57, pp. 10–25.

11. Thakore D. Conflict and conflict management. IOSR J. Bus. Manag, 2013, no. 8, pp. 7–16.

12. Valova Y. I., Krupnov Y. A., Urumova F. M. Ekonomicheskaya konfliktologiya i sovremennaya sotsial'no-ekonomicheskaya sreda [Economic conflict and modern socio-economic environment]. Vestnik Moskovskogo gosudarstvennogo oblastnogo universiteta. Seriya: Ekonomika = Bulletin of the Moscow State Regional University. Series: Economics, 2020, no. 2, pp. 8‒18.

13. Solod A. A., Bogacheva Yu. V. [Economic conflictology and competition]. Sovremennye problemy, tendentsii i perspektivy razvitiya predprinimatel'stva v Rossii. Sbornik nauchnykh trudov prepodavatelei i studentov kafedry ekonomiki i predprinimatel'stva [Modern Problems, Trends and Prospects for the Development of Entrepreneurship in Russia. Collection of Scientific Works of Teachers and Students of the Department of Economics and Entrepreneurship]. Moscow, Moscow State Regional University Publ., 2021, pp. 190‒194. (In Russ.)

14. Valova Y. I. Rol' poznaniya konflikta v sovremennom mire [The role of conflict cognition in the modern world]. International Journal of Professional Science, 2020, no. 8, pp. 20‒24.

15. Molinero X., Riquelme F. Influence decision models: From cooperative game theory to social network analysis. Comput. Sci. Rev., 2021, no. 39, p. 100343.

16. Azam N., Zhang Y., Yao J. Evaluation functions and decision conditions of three-way decisions with game-theoretic rough sets. Eur. J. Oper. Res., 2017, no. 261, pp. 704–714.

17. Liu J., Yu C., Li C., Han J. Cooperation or Conflict in Doctor-Patient Relationship? An Analysis from the Perspective of Evolutionary Game. IEEE Access, 2020, no. 8, pp. 42898–42908.

18. Wang Y., Bu F. Modeling radicalization of terrorism under the influence of multiple ideologies. AIMS Math, 2022, no. 7, pp. 4833–4850.

19. Tench S., Fry H., Gill P. Spatio-temporal patterns of IED usage by the Provisional Irish Republican Army. Eur. J. Appl. Math., 2016, no. 27, pp. 377–402.

20. Guo W. Common statistical patterns in urban terrorism. R. Soc. Open Sci., 2019, no. 6, p. 190645.

21. Qadri, F. Traffic Conflict Modelling at Six Leg Unsignalized Intersection. Proceedings of the 11th Asia Pacific Transportation and the Environment Conference (APTE 2018), Malang, Indonesia, 18– 19 October 2018. Amsterdam, The Netherlands, Atlantis Press, 2018, pp. 58–61.

22. Mastrotheodoros S., Van der Graaff J., Deković M., Meeus W. H., Branje S. Parent–adolescent conflict across adolescence: Trajectories of informant discrepancies and associations with personality types. Journal of Youth and Adolescence, 2020, no. 49, pp. 119‒135.

23. Suo L.-W., Yang H.-L. Three-way conflict analysis based on incomplete situation tables: A tentative study. Int. J. Approx. Reason., 2022, no. 145, pp. 51–74.

24. He X., Wei L., She Y. L-fuzzy concept analysis for three-way decisions: Basic definitions and fuzzy inference mechanisms. Int. J. Mach. Learn. Cybern., 2018, no. 9, pp. 1857–1867.

25. Levin V. I. Logiko-algebraicheskii podkhod k modelirovaniyu konfliktov [Logico-algebraic approach to conflict modeling]. Sistemy upravleniya, svyazi i bezopasnosti = Control, Communication and Security Systems, 2015, no. 4, pp. 69–87.

26. Svetlov V. A. Vvedenie v konfliktologiyu [Introduction to conflictology]. Moscow, Flint Publ., 2018. 520 p.

27. Antipova E. S. Matematicheskoe modelirovanie konfliktov [Mathematical Modeling of Conflicts]. Vestnik Yugorskogo gosudarstvennogo universiteta = Vestnik of Yugra State University, 2023, no. 4, pp. 41‒56. https://doi.org/10.18822/byusu20230441-56