相关论文: Synchronization and Maximum Lyapunov Exponents of …

A general mathematical method is presented for the systematic construction of coupled map lattices (CMLs) out of deterministic cellular automata (CAs). The entire CA rule space is addressed by means of a universal map for CAs that we have…

A major open question in the study of synchronization of coupled oscillators is to find necessary and sufficient condition for a system to synchronize on a given family of graphs. This is a difficult question that requires to understand…

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…

This paper presents an application of the Infinite Unit Axiom, introduced by Yaroslav Sergeyev, (see [11] - [14]) to the development of one-dimensional cellular automata. This application allows the establishment of a new and more precise…

We study general random dynamical systems of continuous maps on some compact metric space. Assuming a local contraction condition and uniqueness of the stationary measure, we establish probabilistic limit laws such as the central limit…

In this paper, we mainly study linear one-dimensional and two-dimensional elementary cellular automata that generate symmetrical spatio-temporal patterns. For spatio-temporal patterns of cellular automata from the single site seed, we…

The paper proposes a simple formalism for dealing with deterministic, non-deterministic and stochastic cellular automata in a unifying and composable manner. Armed with this formalism, we extend the notion of intrinsic simulation between…

We study the dynamical properties of a broad class of high-dimensional random dynamical systems exhibiting chaotic as well as fixed point and periodic attractors. We consider cases in which attractors can co-exists in some regions of the…

Reversible Cellular Automata (RCA) are a physics-like model of computation consisting of an array of identical cells, evolving in discrete time steps by iterating a global evolution G. Further, G is required to be shift-invariant (it acts…

This paper studies three classes of cellular automata from a computational point of view: freezing cellular automata where the state of a cell can only decrease according to some order on states, cellular automata where each cell only makes…

We study a probabilistic cellular automaton to describe two population biology problems: the threshold of species coexistence in a predator-prey system and the spreading of an epidemic in a population. By carrying out time-dependent…

We present results from an experiment similar to one performed by Packard (1988), in which a genetic algorithm is used to evolve cellular automata (CA) to perform a particular computational task. Packard examined the frequency of evolved CA…

Discretizing spacetime is often a natural step towards modelling physical systems. For quantum systems, if we also demand a strict bound on the speed of information propagation, we get quantum cellular automata (QCAs). These originally…

We introduce the property of pre-expansivity for cellular automata (CA): it is the property of being expansive on asymptotic pairs of configurations (i.e. configurations that differ in only finitely many positions). Pre-expansivity…

We study the asymptotic behaviour of symbolic computing systems, notably one-dimensional cellular automata (CA), in order to ascertain whether and at what rate the number of complex versus simple rules dominate the rule space for increasing…

The conditional Lyapunov exponent is defined for investigating chaotic synchronization, in particular complete synchronization and generalized synchronization. We find that the conditional Lyapunov exponent is expressed as a formula in…

We examine the use of synchronization as a mechanism for extracting parameter and state information from experimental systems. We focus on important aspects of this problem that have received little attention previously, and we explore them…

We construct a cellular automaton (CA) model that describes the movement of a particle in a disordered system. The mathematical properties of the CA model were examined by varying the configuration of grid and determining the number of…

Previous study of cellular automata and random Boolean networks has shown emergent behavior occurring at the edge of chaos where the randomness (disorder) of internal connections is set to an intermediate critical value. The value at which…

A synopsis is offered of the properties of discrete and integer-valued, hence "natural", cellular automata (CA). A particular class comprises the "Hamiltonian CA" with discrete updating rules that resemble Hamilton's equations. The…