Related papers: Point Mutations and Transitions Between Cellular A…
The deterministic dynamics of randomly connected neural networks are studied, where a state of binary neurons evolves according to a discreet-time synchronous update rule. We give a theoretical support that the overlap of systems' states…
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…
We explore some aspects of phase transitions in cellular automata. We start recalling the standard formulation of statistical mechanics of discrete systems (Ising model), illustrating the Monte Carlo approach as Markov chains and stochastic…
In a standard bifurcation of a dynamical system, the stationary points (or more generally attractors) change qualitatively when varying a control parameter. Here we describe a novel unusual effect, when the change of a parameter, e.g. a…
Cellular Automata are discrete--time dynamical systems on a spatially extended discrete space which provide paradigmatic examples of nonlinear phenomena. Their stochastic generalizations, i.e., Probabilistic Cellular Automata, are discrete…
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 cellular automata discrete dynamical system is considered as the two-stage process: the majority rule for the change in the automata state and the rule for the change in topological relations between automata. The influence of changing…
We discuss various properties of Probabilistic Cellular Automata, such as the structure of the set of stationary measures and multiplicity of stationary measures (or phase transition) for reversible models.
Markov switching models are a popular family of models that introduces time-variation in the parameters in the form of their state- or regime-specific values. Importantly, this time-variation is governed by a discrete-valued latent…
We present a family of one-dimensional cellular automata modeling the diffusion of an innovation in a population. Starting from simple deterministic rules, we construct models parameterized by the interaction range and exhibiting a…
The spatial structure, fluctuations as well as all state probabilities of self-organized (steady) states of cellular automata can be found (almost) exactly and {\em explicitly} from their Markovian dynamics. The method is shown on an…
In this paper we present two interesting properties of stochastic cellular automata that can be helpful in analyzing the dynamical behavior of such automata. The first property allows for calculating cell-wise probability distributions over…
The transition structure of an automaton can be used to create a natural topology to the set of states of an automaton, generating, this way, a topological space. Probabilistic automata can also be modeled in terms of measure theory. A…
Markov branching systems form a fundamental class of stochastic models that are extensively applied in biology, physics, finance, and other domains. These systems are distinguished by their continuous-time evolution and inherent branching…
The probabilities of transitions of the system to the different final states are determined by the values of the amplitudes of the corresponding individual states during stimulated recombination of atoms.
We consider the problem of metastability for stochastic reversible dynamics with exponentially small transition probabilities. We generalize previous results in several directions. We give an estimate of the spectral gap of the transition…
The probabilistic cellular automaton (PCA) method is highlighted for its relatively simple numerical algorithm and low computational cost in the simulation of microstructural evolution. In this method, probabilistic state change rules are…
The bacteria metabolic process of open nonlinear dissipative system far from equilibrium point is modeled using classical methods of synergetics. The invariant measure and its convergence in the phase space of the system was obtained in…
We propose a general approach to study spin models with two symmetric absorbing states. Starting from the microscopic dynamics on a square lattice, we derive a Langevin equation for the time evolution of the magnetization field, that…
We introduce a new class of probabilistic cellular automata that are capable of exhibiting rich dynamics such as synchronization and ergodicity and can be easily inferred from data. The system is a finite-state locally interacting Markov…