Skip to main content
SpringerLink
Log in

A Model of Conflict Society with External Influence

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

We study a mathematical model of abstract society with redistribution of the social energy of individuals determined by two factors, namely, by the mutual competition and the presence of external influence. The behavior of the analyzed model is described by relatively simple iterative equations generating a dynamic system with discrete time. Fixed points of the system are determined. For some of these points that are attractors, their pools are partially described. In the general case, we prove the convergence of trajectories to the equilibrium states. In particular, it is shown that the individuals with the highest initial energy are doomed to be defeated if one of weaker individuals receives a sufficiently strong external support. Four examples are discussed to illustrate the most interesting cases of external influence on the dynamics of competition between individuals in an abstract society.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. T. V. Karataeva and V. D. Koshmanenko, “Society, mathematical model of a dynamical system of conflict,” Nelin. Kolyv., 22, No. 1, 66–85 (2019); English translation: J. Math. Sci., 247, No. 2, 291–313 (2020); https://doi.org/10.1007/s10958-020-04803-3.

  2. V. Koshmanenko, T. Karataieva, N. Kharchenko, and I. Verygina, “Models of the conflict redistribution of vital resources,” in: Social Simulation Conf. (Rome, Italy, 2016).

  3. V. Koshmanenko and E. Pugacheva, “Conflict interactions with external intervention,” in: Social Simulation Conf. (Rome, Italy, 2016).

  4. V. D. Koshmanenko and T. V. Karataieva, “On personal strategies in conflict socium,” in: Econophysics Colloq. (Warsaw, July 5–7, 2017), p. 32.

  5. I. V. Veryhina and V. D. Koshmanenko, “Problem of optimal strategy in the models of conflict redistribution of the resource space,” Ukr. Mat. Zh., 69, No. 7, 905–911 (2017); English translation: Ukr. Math. J., 69, No. 7, 1051–1059 (2017); https://doi.org/10.1007/s11253-017-1414-7.

  6. V. D. Koshmanenko and O. R. Satur, “Sure event problem in multicomponent dynamical systems with attractive interaction,” Nelin. Kolyv., 22, No. 2, 220–234 (2019); English translation: J. Math. Sci., 249, No. 4, 629–646 (2020); https://doi.org/10.1007/s10958-020-04962-3.

  7. T. Karataieva, V. Koshmanenko, M. J. Krawczyk, and K. Kulakowski, “Mean field model of a game for power,” Phys. A, 525, 535–547 (2019); https://doi.org/10.1016/j.physa.2019.03.110.

  8. S. Albeverio, M. V. Bodnarchyk, and V. Koshmanenko, “Dynamics of discrete conflict interactions between non-annihilating opponents,” Methods Funct. Anal. Topol., 11, No. 4, 309–319 (2005).

    MathSciNet  MATH  Google Scholar 

  9. S. Albeverio, V. Koshmanenko, and I. Samoilenko, “The conflict interaction between two complex systems: Cyclic migration,” J. Interdiscip. Math., 11, No. 2, 163–185 (2008).

    Article  MathSciNet  MATH  Google Scholar 

  10. V. D. Koshmanenko and I. V. Samoilenko, “Model of a dynamical system of a conflict triad,” Nelin. Kolyv., 14, No. 1, 55–75 (2011); English translation: Nonlin. Oscillat., 14, No. 1, 56–76 (2011).

  11. R. Axelrod, “The dissemination of culture: a model with local convergence and global polarization,” J. Conflict Resolut., 41, No. 2, 203–226 (1997); https://doi.org/10.1177/0022002797041002001.

    Article  Google Scholar 

  12. N. Bellomo, M. Herrero, and A. Tosin, “On the dynamics of social conflicts: looking for the black swan,” Kinet. Relat. Models, 6, No. 3, 459–479 (2013).

    Article  MathSciNet  MATH  Google Scholar 

  13. N. Bellomo and J. Soler, “On the mathematical theory of the dynamics of swarms viewed as complex systems,” Math. Models Meth. Appl. Sci., 22, 29 p. (2012).

  14. N. Bellomo, F. Brezzi, and M. Pulvirenti, “Modeling behavioral social systems,” Math. Models Meth. Appl. Sci., 27, No. 1, 1–11 (2017); https://doi.org/10.1142/S0218202517020018.

    Article  MathSciNet  MATH  Google Scholar 

  15. G. I. Bischi and F. Tramontana, “Three-dimensional discrete-time Lotka–Volterra models with an application to industrial clusters,” Comm. Nonlin. Sci. Numer. Simul., 15, 3000–3014 (2010).

  16. P. T. Coleman, R. Vallacher, A. Nowak, and L. Bui-Wrzosinska, “Interactable conflict as an attractor: presenting a dynamical-systems approach to conflict, escalation, and interactability,” IACM Meeting Paper (2007).

  17. J. M. Epstein, Nonlinear Dynamics, Mathematical Biology, and Social Science, Addison-Wesley Publ. Comp., Reading (1997).

    MATH  Google Scholar 

  18. J. M. Epstein, “Modeling civil violence: An agent-based computational approach,” Proc. Nat. Acad. Sci. USA, 99, No. 3, 7243–7250 (2002).

    Article  Google Scholar 

  19. J. M. Epstein, “Why model?,” J. Artif. Soc. Soc. Simul., 11, No. 412 (2008).

  20. A. Flache, M. Mäs, T. Feliciani, E. Chattoe-Brown, G. Deffuant, S. Huet, and J. Lorenz, “Models of social influence: towards the next frontiers,” J. Artif. Soc. Soc. Simul., 20(4), 2JASSS (2017); https://doi.org/10.18564/jasss.3521.

  21. N. E. Friedkin and E. C. Johnsen, Social Influence Network Theory, Cambridge Univ. Press, New York (2011); https://doi.org/10.1017/CBO9780511976735.

    Book  MATH  Google Scholar 

  22. H.Hu, “Competing opinion diffusion on social networks,” R. Soc. Open Sci., 4, 171160 (2017); https://doi.org/10.1098/rsos.171160.

  23. H.-B. Hu and X.-F. Wang, “Discrete opinion dynamics on networks based on social influence,” J. Phys. A, 42, No. 225005 (2009); https://doi.org/10.1088/1751-8113/42/22/225005.

  24. M. Jalili, “Social power and opinion formation in complex networks,” Phys. A, 392, 959–966 (2013); https://doi.org/10.1016/j.physa.2012.10.013.

  25. K. I. Takahashi and K. Md. M. Salam, “Mathematical model of conflict with non-annihilating multi-opponent,” J. Interdiscip. Math., 9, No. 3, 459–473 (2006).

    MathSciNet  MATH  Google Scholar 

  26. S. Md. M. Khan and K. I. Takahashi, “Segregation through conflict,” Adv. Appl. Sociol., 3, No. 8, 315–319 (2013).

    Article  Google Scholar 

  27. V. D. Koshmanenko, “Theorem on conflict for a pair of stochastic vectors,” Ukr. Mat. Zh., 55, No. 4, 555–560 (2003); English translation: Ukr. Math. J., 55, No. 4, 671–678 (2003).

  28. V. Koshmanenko, “Theorem of conflicts for a pair of probability measures,” Math. Methods Oper. Res., 59, No. 2, 303–313 (2004).

    Article  MathSciNet  MATH  Google Scholar 

  29. V. D. Koshmanenko, Spectral Theory of Dynamical Conflict Systems [in Ukrainian], Naukova Dumka, Kyiv (2016).

    MATH  Google Scholar 

  30. S. A. Marvel, H. Hong, A. Papush, and S. H. Strogatz, “Encouraging moderation: clues from a simple model of ideological conflict,” Phys. Rev. Lett., 109, 118702 (2012); https://doi.org/10.1103/PhysRevLett.109.118702.

  31. S. Thurner, R. Hanel, and P. Klimek, Introduction to the Theory of Complex Systems, Oxford Univ. Press, Oxford (2018).

    Book  MATH  Google Scholar 

  32. T. C. Schelling, The Strategy of Conflict, Harvard Univ. Press, Cambridge (1980).

    MATH  Google Scholar 

  33. V. Koshmanenko, “Formula of conflict dynamics,” in: Proc. of the Institute of Mathematics, National Academy of Sciences of Ukraine [in Ukrainian], 17, No. 2 (2020), pp. 113–149.

  34. P. Ashwin, C. Bick, and O. Burylko, “Identical phase oscillator networks: bifurcations, symmetry, and reversibility for generalized coupling,” Front. Appl. Math. Stat., 2, No. 7 (2016).

  35. O. A. Burylko, “Collective dynamics and bifurcations in symmetric networks of phase oscillators. I,” Nelin. Kolyv., 22, No. 2, 165–195 (2019); English translation: J. Math. Sci., 249, No. 4, 573–600 (2020).

  36. O. A. Burylko, “Collective dynamics and bifurcations in symmetric networks of phase oscillators. II,” Nelin. Kolyv., 22, No. 3, 312–340 (2019); English translation: J. Math. Sci., 253, No. 2, 204–229 (2021); https://doi.org/10.1007/s10958-021-05223-7.

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Ukrainian National Academy of Sciences, Tereshchenkivs’ka Str., 3, Kyiv, 01024, Ukraine

    T. V. Karataeva & V. D. Koshmanenko

  2. Drahomanov National Pedagogic University, Pyrohov Str., 9, Kyiv, 01601, Ukraine

    V. D. Koshmanenko

Authors
  1. T. V. Karataeva
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. V. D. Koshmanenko
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to V. D. Koshmanenko.

Additional information

Translated from Neliniini Kolyvannya, Vol. 24, No. 3, pp. 342–362, July–September, 2021.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Karataeva, T.V., Koshmanenko, V.D. A Model of Conflict Society with External Influence. J Math Sci 272, 244–266 (2023). https://doi.org/10.1007/s10958-023-06414-0

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-023-06414-0

Search

Navigation