Dynamical Systems on Honeycombs

  • Valery V. Kozlov
  • Alexander P. Buslaev
  • Alexander G. Tatashev
  • Marina V. Yashina
Conference paper


Stochastic and deterministic versions of a discrete dynamical system on a necklace network are investigated. This network contains several contours. There are three cells and a particle on each contour. The particle occupies one of the cells and, at each step, it makes an attempt to move to the next cell in the direction of movement. As well as on neighboring contours the particles move in accordance with rules of stochastic or deterministic type. We prove that the behavior of the model with a rule of the first type is stochastic only at the beginning, and after a time interval the behavior becomes purely deterministic. The system with a rule of the first type reaches a stationary mode which depends on the initial state. The average velocity of particles and other characteristics of the dynamical systems are studied.


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Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  • Valery V. Kozlov
    • 1
  • Alexander P. Buslaev
    • 2
  • Alexander G. Tatashev
    • 2
  • Marina V. Yashina
    • 2
  1. 1.Steklov Mathematical InstituteRussian Academy of SciencesMoscowRussia
  2. 2.MADIMTUCIMoscowRussia

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