Convergence to equilibrium attractor in models of dynamic confl ict systems with attractive interaction

Authors

DOI:

https://doi.org/10.15407/dopovidi2023.03.003

Keywords:

dynamic conflict system, difference equation, conflict interaction (composition or mapping), attractive interaction, fixed point, limit state, stability of limit state, discrete measure, stochastic vector.

Abstract

This study focuses on the construction of a model for dynamic conflict systems with attractive interaction. The behavior of trajectories in this system is influenced by a set of positive parameters. The existence of equilibrium states is proven, and their properties are examined. An explicit form of equilibrium states is established, and the issue of stability is investigated.

Downloads

Download data is not yet available.

References

Karataeva, T. V. & Koshmanenko, V. D. (2020). Society, mathematical model of a dynamical system of conflict. J. Math. Sci., 247, pp. 291-313. https://doi.org/10.1007/s10958-020-04803-3

Karataieva, T., Koshmanenko, V., Krawczyk, M. & Kulakowski, K. (2019).Mean field model of a game for power. Physica A, 525, pp. 535-547. https://doi.org/10.1016/j.physa.2019.03.110

Koshmanenko, V. (2016). Spectral Theory for Conflict Dynamical Systems (in Ukrainian). Kyiv: Naukova Dumka.

Schwerdtfeger, F. (1968). Ökologie der Tiere, Bd. II: Demökologie. Struktur und Dynamik tierischer Popu-lationen. Berlin: Paul Parey Vlg.

Hu, H. (2017). Competing opinion diffusion on social networks. R. Soc. Open Sci., 4, No. 11. https://doi.org/10.1098/rsos.171160

Moinet, A., Barrat, B. & Pastor-Satorras, R. (2018). Generalized voterlike model on activity-driven networks with attractiveness. Phys. Rev. E., 98, 022303, 9 p. https://doi.org/10.1103/PhysRevE.98.022303

Satur, O. R. & Kharchenko, N. V. (2020). The model of dynamical system for the attainment of consensus. Ukr. Math. J., 71, No. 9, pp. 1456-1469. https://doi.org/10.1007/s11253-020-01725-w

Satur, О. R. (2021). Dependence of the behavior of the trajectories of dynamic conflict systems on the interaction vector. Nonlinear Oscillations, 25, No. 1, pp. 72-88.

Burylko, O. (2020). Collective dynamics and bifurcations in symmetric networks of phase oscillators. I. J. Math. Sci., 249, No. 4, pp. 573-600. https://doi.org/10.1007/s10958-020-04959-y

Burylko, O. (2021). Collective dynamics and bifurcations in symmetric networks of phase oscillators. II. J. Math. Sci., 253, No. 2, pp. 204-229. https://doi.org/10.1007/s10958-021-05223-7

Published

11.07.2023

How to Cite

Satur, O. (2023). Convergence to equilibrium attractor in models of dynamic confl ict systems with attractive interaction. Reports of the National Academy of Sciences of Ukraine, (3), 3–8. https://doi.org/10.15407/dopovidi2023.03.003