Fixed points of complex systems with attractive interaction

Authors

  • V. D. Koshmanenko Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine https://orcid.org/0000-0003-0411-4059
  • N. Kharchenko Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Tereshchenkivs’ka, Kyiv, 01601, Ukraine  

DOI:

Keywords:

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

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.

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Published

2017-06-25

Issue

Vol. 23 No. 2 (2017)

Section

Articles

How to Cite

Koshmanenko, V. D., and N. Kharchenko. “Fixed Points of Complex Systems With Attractive Interaction”. Methods of Functional Analysis and Topology, vol. 23, no. 2, June 2017, pp. 164-76, https://zen.imath.kiev.ua/index.php/mfat/article/view/661.