Related papers: Cellular Automata model for period-$n$ synchroniza…
We study the nature of the synchronization transition in spatially extended systems by discussing a simple stochastic model. An analytic argument is put forward showing that, in the limit of discontinuous processes, the transition belongs…
Cellular Automata have been used since their introduction as a discrete tool of modelization. In many of the physical processes one may modelize thus (such as bootstrap percolation, forest fire or epidemic propagation models, life without…
Systems with absorbing (trapped) states may exhibit a nonequilibrium phase transition from a noise-free inactive phase into an ever-lasting active phase. We briefly review the absorbing critical phenomena and universality classes, and…
We investigate the percolation properties of a two-state (occupied - empty) cellular automaton, where at each time step a cluster of occupied sites is removed and the same number of randomly chosen empty sites are occupied again. We find a…
Using Pade approximations and Monte Carlo simulations, we study the phase diagram of the Two-Neighbor Stochastic Cellular Automata, which have two parameters $p_{1}$ and $p_{2}$ and include the mixed site-bond directed percolation (DP) as a…
A transition from asymmetric to symmetric patterns in time-dependent extended systems is described. It is found that one dimensional cellular automata, started from fully random initial conditions, can be forced to evolve into complex…
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…
We determine the first through fourth moments of the order parameter, and various ratios, for several one- and two-dimensional models with absorbing-state phase transitions. We perform a detailed analysis of the system-size dependence of…
We numerically study a directed small-world network consisting of attractively coupled, identical phase oscillators. While complete synchronization is always stable, it is not always reachable from random initial conditions. Depending on…
We present the simplest discrete model to date that leads to synchronization of stochastic phase-coupled oscillators. In the mean field limit, the model exhibits a Hopf bifurcation and global oscillatory behavior as coupling crosses a…
A cellular automaton model is presented for random walkers with biologically motivated interactions favoring local alignment and leading to collective motion or swarming behavior. The degree of alignment is controlled by a sensitivity…
This review addresses recent developments in nonequilibrium statistical physics. Focusing on phase transitions from fluctuating phases into absorbing states, the universality class of directed percolation is investigated in detail. The…
One-dimensional cellular automata are discrete dynamical systems that operate on an infinite lattice of sites and are characterized by the locality and uniformity of their update rule. Permutations of the state set and isometric…
Discrete dynamical systems can exhibit complex behaviour from the iterative application of straightforward local rules. A famous example are cellular automata whose global dynamics are notoriously challenging to analyze. To address this, we…
Probabilistic cellular automata provide a simple framework for the exploration of classical nonequilibrium processes. Recently, quantum cellular automata have been proposed that rely on the propagation of a one-dimensional quantum state…
A probabilistic cellular automaton for cargo transport is presented that generalizes the totally asymmetric exclusion process with a defect from continuous time to parallel dynamics. It appears as an underlying principle in cellular…
We propose and investigate a one-parameter probabilistic mixture of one-dimensional elementary cellular automata under the guise of a model for the dynamics of a single-species unstructured population with nonoverlapping generations in…
We improve a recently proposed dynamically driven renormalization group algorithm for cellular automata systems with one absorbing state, introducing spatial correlations in the expression for the transition probabilities. We implement the…
We show that local structure approximation of sufficiently high order can predict the existence of second order phase transitions belonging to the directed percolation university class in $\alpha$-asynchronous cellular automata.
A recent study of conserved Manna model, with both discrete and continuous variable, indicates that absorbing phase transitions therein belong to the directed percolation (DP) universality class. In this context we revisit critical…