Related papers: Increasing coupling of probabilistic cellular auto…
In this paper, we revisit a classic example of probabilistic cellular automaton (PCA) on {0, 1} Z , namely, addition modulo 2 of the states of the left-and right-neighbouring cells, followed by either preserving the result of the addition,…
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 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 study the relationship between the partial synchronous (PaS) state and the coupling structure in general dynamical systems. By the exact proof, we find the sufficient and necessary condition of the existence of PaS state for the coupling…
The synchronization of two stochastically coupled one-dimensional cellular automata (CA) is analyzed. It is shown that the transition to synchronization is characterized by a dramatic increase of the statistical complexity of the patterns…
We study the relationship between the partially synchronous state and the coupling structure in general dynamical systems. Our results show that, on the contrary to the widely accepted concept, topological symmetry in a coupling structure…
We revisit the problem of finding the conditions under which synchronous probabilistic cellular automata indexed by the line $\mathbb{Z}$, or the periodic line $\cyl{n}$, depending on 2 neighbours, admit as invariant distribution the law of…
A synchronization mechanism driven by annealed noise is studied for two replicas of a coupled-map lattice which exhibits stable chaos (SC), i.e. irregular behavior despite a negative Lyapunov spectrum. We show that the observed…
We demonstrate that the concept of a conservation law can be naturally extended from deterministic to probabilistic cellular automata (PCA) rules. The local function for conservative PCA must satisfy conditions analogous to conservation…
This study introduces Skewed Fully Asynchronous Cellular Automata (SACA), a novel update scheme in cellular automata that updates the states of only two consecutive and adjacent cells, such as ci and ci+1, simultaneously at each time step.…
In this paper a new form of duality for probabilistic cellular automata (PCA) is introduced. Using this duality, an ergodicity result for processes having a dual is proved. Also, conditions on the probabilities defining the evolution of the…
We investigate one-dimensional elementary probabilistic cellular automata (PCA) whose dynamics in first-order mean-field approximation yields discrete logisticlike growth models for a single-species unstructured population with…
We consider the problem of approximate sampling from the finite volume Gibbs measure with a general pair interaction. We exhibit a parallel dynamics (Probabilistic Cellular Automaton) which efficiently implements the sampling. In this…
Coupling is a widely used technique in the theoretical study of interacting stochastic processes. In this paper I present an example demonstrating its usefulness also in the efficient computer simulation of such processes. I first describe…
We have developed a simple cellular automata model for nonlinearly coupled phase oscillators which can exhibit many important collective dynamical states found in other synchronizing systems. The state of our system is specified by a set of…
For a general attractive Probabilistic Cellular Automata on S Z d , we prove that the (time-) convergence towards equilibrium of this Markovian parallel dynamics, exponentially fast in the uniform norm, is equivalent to a condition (A).…
Cellular automata (CA) consist of an array of identical cells, each of which may take one of a finite number of possible states. The entire array evolves in discrete time steps by iterating a global evolution G. Further, this global…
The searching for the stable patterns in the evolution of cellular automata is implemented using stochastic synchronization between the present structures of the system and its precedent configurations. For most of the known evolution rules…
This paper introduces a simple formalism for dealing with deterministic, non- deterministic and stochastic cellular automata in an unified and composable manner. This formalism allows for local probabilistic correlations, a feature which is…
We show that there exists a one-to-one correspondence between the set of number-conserving cellular automata (CA) with $q$ inputs and the set of balanced sequences with $q$ terms. This allows to enumerate number-conserving CA. We also show…