The ergodic theory of cellular automata
M Pivato - International Journal of General Systems, 2012 - Taylor & Francis
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The ergodic theory of traffic jams
L Gray, D Griffeath - Journal of statistical Physics, 2001 - Springer
We introduce and analyze a simple probabilistic cellular automaton which emulates the flow
of cars along a highway. Our Traffic CA captures the essential features of several more …
of cars along a highway. Our Traffic CA captures the essential features of several more …
On discrete flow networks model spectra: statements, simulation, hypotheses
AP Buslaev, MJ Fomina, AG Tatashev… - Journal of Physics …, 2018 - iopscience.iop.org
A deterministic dynamical system is considered. A supporter of the system is a closedchain
of contours. There are N= 2n cells and particles cluster on each contour. Each cluster …
of contours. There are N= 2n cells and particles cluster on each contour. Each cluster …
Metric properties of discrete time exclusion type processes in continuum
M Blank - Journal of Statistical Physics, 2010 - Springer
A new class of exclusion type processes acting in continuum with synchronous updating is
introduced and studied. Ergodic averages of particle velocities are obtained and their …
introduced and studied. Ergodic averages of particle velocities are obtained and their …
Spectral cycles and average velocity of clusters in discrete two‐contours system with two nodes
MV Yashina, AG Tatashev - Mathematical Methods in the …, 2020 - Wiley Online Library
The paper considers a discrete dynamical system containing two contours. There are n cells
and m particles in each contour. At any time, the particles of each contour form a cluster …
and m particles in each contour. At any time, the particles of each contour form a cluster …
Spectrum of elementary cellular automata and closed chains of contours
A Tatashev, M Yashina - Machines, 2019 - mdpi.com
In this paper, we study the properties of some elementary automata. We have obtained the
characteristics of these cellular automata. The concept of the spectrum for a more general …
characteristics of these cellular automata. The concept of the spectrum for a more general …
Density classification on infinite lattices and trees
A Bušić, N Fates, J Mairesse, I Marcovici - LATIN 2012: Theoretical …, 2012 - Springer
Consider an infinite graph with nodes initially labeled by independent Bernoulli random
variables of parameter p. We want to find a (probabilistic or deterministic) cellular automaton …
variables of parameter p. We want to find a (probabilistic or deterministic) cellular automaton …
Exact results for discrete dynamical systems on a pair of contours
AP Buslaev, AG Tatashev - Mathematical Methods in the …, 2018 - Wiley Online Library
The study of discrete model of movement on a single contour, equivalent to CA 184 in terms
of Wolfram cellular automata classification, was conducted in the late 1990s and early …
of Wolfram cellular automata classification, was conducted in the late 1990s and early …
On cellular automata, traffic and dynamical systems in graphs
AP Buslaev, AG Tatashev, MV Yashina - International Journal of …, 2018 - elibrary.ru
Qualitative studies of discrete dynamical systems behavior on networks are relevant in many
fields such as system biology, transportation, information traffic, material sciences and so on …
fields such as system biology, transportation, information traffic, material sciences and so on …
The discrete-time facilitated totally asymmetric simple exclusion process
S Goldstein, JL Lebowitz, ER Speer - arXiv preprint arXiv:2003.04995, 2020 - arxiv.org
We describe the translation invariant stationary states of the one dimensional discrete-time
facilitated totally asymmetric simple exclusion process (F-TASEP). In this system a particle at …
facilitated totally asymmetric simple exclusion process (F-TASEP). In this system a particle at …