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Fixed points of complex systems with attractive interaction


Abstract

We study the behavior of complex dynamical systems describing an attractive interaction between two opponents. We use the stochastic interpretation and describe states of systems in terms of probability distributions (measures) and their densities. For the time evolution we derive specific non-linear difference equations which generalize the well-known Lotka-Volterra equations. Our results state the existence of fixed points (equilibrium states) for various kinds of attractive interactions. Besides, we present an explicit description of the limiting distributions and illustrate abstract results by several examples.

Key words: Complex system, dynamical system, fixed point, conflict, agent, resource space, attractive interaction, probability measure, difference equation.


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Article Information

TitleFixed points of complex systems with attractive interaction
SourceMethods Funct. Anal. Topology, Vol. 23 (2017), no. 2, 164-176
MilestonesReceived 07/03/2017
CopyrightThe Author(s) 2017 (CC BY-SA)

Authors Information

V. Koshmanenko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine

N. Kharchenko
Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine  


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Citation Example

V. Koshmanenko and N. Kharchenko, Fixed points of complex systems with attractive interaction, Methods Funct. Anal. Topology 23 (2017), no. 2, 164-176.


BibTex

@article {MFAT970,
    AUTHOR = {V. Koshmanenko and N. Kharchenko},
     TITLE = {Fixed points of complex systems with attractive interaction},
   JOURNAL = {Methods Funct. Anal. Topology},
  FJOURNAL = {Methods of Functional Analysis and Topology},
    VOLUME = {23},
      YEAR = {2017},
    NUMBER = {2},
     PAGES = {164-176},
      ISSN = {1029-3531},
       URL = {http://mfat.imath.kiev.ua/article/?id=970},
}


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