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Self-organization with small range interactions: Equilibria and creation of bipolarity

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  • Lachowicz, Mirosław
  • Leszczyński, Henryk
  • Topolski, Krzysztof A.

Abstract

We study a kinetic equation which describes self-organization of various complex systems, assuming the interacting rate with small support. This corresponds to interactions between an agent with a given internal state and agents having short distance states only. We identify all possible stationary (equilibrium) solutions and describe the possibility of creating of bipolar (bimodal) distribution that is able to capture interesting behavior in modeling systems, e.g. in political sciences.

Suggested Citation

  • Lachowicz, Mirosław & Leszczyński, Henryk & Topolski, Krzysztof A., 2019. "Self-organization with small range interactions: Equilibria and creation of bipolarity," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 156-166.
    • Handle: RePEc:eee:apmaco:v:343:y:2019:i:c:p:156-166
    DOI: 10.1016/j.amc.2018.09.050
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    References listed on IDEAS

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    1. Soares, Helena & Sequeira, Tiago Neves & Marques, Pedro Macias & Gomes, Orlando & Ferreira-Lopes, Alexandra, 2018. "Social infrastructure and the preservation of physical capital: Equilibria and transitional dynamics," Applied Mathematics and Computation, Elsevier, vol. 321(C), pages 614-632.
    2. Wang, Shaoli & Rong, Libin & Wu, Jianhong, 2016. "Bistability and multistability in opinion dynamics models," Applied Mathematics and Computation, Elsevier, vol. 289(C), pages 388-395.
    3. Wagner, R. Harrison, 1993. "What was bipolarity?," International Organization, Cambridge University Press, vol. 47(1), pages 77-106, January.
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    Cited by:

    1. Mirosław Lachowicz & Henryk Leszczyński, 2020. "Modeling Asymmetric Interactions in Economy," Mathematics, MDPI, vol. 8(4), pages 1-14, April.
    2. Lachowicz, Mirosław & Matusik, Milena & Topolski, Krzysztof A., 2024. "Population of entities with three individual states and asymmetric interactions," Applied Mathematics and Computation, Elsevier, vol. 464(C).
    3. Lachowicz, Mirosław & Leszczyński, Henryk & Topolski, Krzysztof A., 2022. "Approximations of kinetic equations of swarm formation: Convergence and exact solutions," Applied Mathematics and Computation, Elsevier, vol. 417(C).

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