Related papers: Competing deterministic growth models in two dimen…
A point $p \in \mathbb{R}^d$ is said to dominate another point $q \in \mathbb{R}^d$ if the coordinate of $p$ is greater than or equal to the coordinate of $q$ in every dimension. A set of points in $\mathbb{R}^d$ is dominance-free if any…
We give new sufficient ergodicity conditions for two-state probabilistic cellular automata (PCA) of any dimension and any radius. The proof of this result is based on an extended version of the duality concept. Under these assumptions, in…
We study the cyclic cellular automaton (CCA) and the Greenberg-Hastings model (GHM) with $\kappa\ge 3$ colors and contact threshold $\theta\ge 2$ on the infinite $(d+1)$-regular tree, $T_d$. When the initial state has the uniform product…
We give a necessary and sufficient condition for the existence of an increasing coupling of $N$ ($N \geq 2$) synchronous dynamics on $S^{\mathbb Z^d}$(PCA). Increasing means the coupling preserves stochastic ordering. We first present our…
Topological dynamics of cellular automata (CA), inherited from classical dynamical systems theory, has been essentially studied in dimension 1. This paper focuses on higher dimensional CA and aims at showing that the situation is different…
We investigate the phase transitions in a one-dimensional system with colored noise. Previous studies indicated that the phase diagram of this system included extended and disorder-induced localized phases. However, by studying the…
The dynamics of a two-qubit system is considered with the aim of a general categorization of the different ways in which entanglement can disappear in the course of the evolution, e.g., entanglement sudden death. The dynamics is described…
We show that cellular automata can classify data by inducing a form of dynamical phase coexistence. We use Monte Carlo methods to search for general two-dimensional deterministic automata that classify images on the basis of activity, the…
Cell cultures exhibit rich and complex behaviors driven by dynamic metabolic interactions among cells. In this work, we present a model that captures these interactions through a framework inspired by statistical mechanics. Using Monte…
We investigate the emergence of sustained spatio-temporal behaviors in reaction-phase separation systems. We focus on binary systems, in which either one or both species can phase separate, and we discuss the stability of the homogeneous…
We consider stochastic rules of mass transport which lead to steady states that factorize over the links of a one-dimensional ring. Based on the knowledge of the steady states, we derive the onset of a phase transition from a liquid to a…
We study a driven zero range process which models a closed system of attractive particles that hop with site-dependent rates and whose steady state shows a condensation transition with increasing density. We characterise the dynamical…
Suppose each site on a one-dimensional chain with periodic boundary condition may take on any one of the states $0,1,..., n-1$, can you find out the most frequently occurring state using cellular automaton? Here, we prove that while the…
We introduce a spatial economic growth model where space is described as a network of interconnected geographic locations and we study a corresponding finite-dimensional optimal control problem on a graph with state constraints. Economic…
An exact characterization of the different dynamical behavior that exhibit the space phase of a reversible and conservative cellular automaton, the so called Q2R model, is shown in this paper. Q2R is a cellular automaton which is a…
The effect of the on-ramp and off-ramp positions $i_1$ and $i_2$, respectively, on the one dimensional-cellular automaton traffic flow behaviour, is investigated numerically. The on-ramp and off-ramp rates at $i_1$ and $i_2$ are $\alpha_0$…
We say that a Cellular Automata (CA) is coalescing when its execution on two distinct (random) initial configurations in the same asynchronous mode (the same cells are updated in each configuration at each time step) makes both…
We investigate a model of interacting clusters which compete for growth. For a finite assembly of coupled clusters, the largest one always wins, so that all but this one die out in a finite time. This scenario of `survival of the biggest'…
The density classification problem is one of the simplest yet non-trivial computing tasks which seem to be ideally suitable for cellular automata (CA). Unfortunately, there exists no one-dimensional two-state CA which classifies binary…
We present a stochastic approach to modeling the dynamics of coexistence of prey and predator populations. It is assumed that the space of coexistence is explicitly subdivided in a grid of cells. Each cell can be occupied by only one…