相关论文: Asymptotic behavior of dynamical systems and cellu…

Cellular Automata (CA) are discrete dynamical systems and an abstract model of parallel computation. The limit set of a cellular automaton is its maximal topological attractor. A well know result, due to Kari, says that all nontrivial…

In this article, we consider a topological dynamical system. The generic limit set is the smallest closed subset which has a comeager realm of attraction. We study some of its topological properties, and the links with equicontinuity and…

This tutorial is about cellular automata that exhibit 'cold dynamics'. By this we mean zero entropy, stabilization of all orbits, trivial asymptotic dynamics, etc. These are purely transient irreversible dynamics, but they capture many…

We study the generic limit sets of one-dimensional cellular automata, which intuitively capture their asymptotic dynamics while discarding transient phenomena. As our main results, we characterize the automata whose generic limit set is a…

We study the set of strictly periodic points in surjective cellular automata, i.e., the set of those configurations which are temporally periodic for a given automaton but they not spatially periodic. This set turns out to be dense for…

Standard dynamical systems theory is centred around the coordinate-invariant asymptotic-time properties of autonomous systems. We identify three limitations of this approach. Firstly, we discuss how the traditional approach cannot take into…

The generic limit set of a topological dynamical system of the smallest closed subset of the phase space that has a comeager realm of attraction. It intuitively captures the asymptotic dynamics of almost all initial conditions. It was…

We consider discrete dynamical systems and lattice models in statistical mechanics from the point of view of their symmetry groups. We describe a C program for symmetry analysis of discrete systems. Among other features, the program…

We study the dynamics of discrete-time regulatory networks on random digraphs. For this we define ensembles of deterministic orbits of random regulatory networks, and introduce some statistical indicators related to the long-term dynamics…

To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…

We say that a finite asynchronous cellular automaton (or more generally, any sequential dynamical system) is pi-independent if its set of periodic points are independent of the order that the local functions are applied. In this case, the…

We study the asymptotic behavior, as time t goes to infinity, of nonautonomous dynamical systems involving multiscale features. These systems model the emergence of various collective behaviors in game theory, as well as the asymptotic…

Let $(X,f_{1,\infty})$ be a nonautonomous dynamical system. In this paper we summarize known definitions of periodic points for general nonautonomous dynamical systems and propose a new, very natural, definition of asymptotic periodicity.…

In order to develop systems capable of artificial evolution, we need to identify which systems can produce complex behavior. We present a novel classification method applicable to any class of deterministic discrete space and time dynamical…

Dynamical systems theory is especially well-suited for determining the possible asymptotic states (at both early and late times) of cosmological models, particularly when the governing equations are a finite system of autonomous ordinary…

We study the computational problem of rigorously describing the asymptotic behaviour of topological dynamical systems up to a finite but arbitrarily small pre-specified error. More precisely, we consider the limit set of a typical orbit,…

We conceive finite automata as dynamical systems on discontinuum and investigate their factors. Factors of finite automata include many well-known simple dynamical systems, e.g. hyperbolic systems and systems with finite attractors. In the…

Cellular automata are a set of computational models in discrete space that have a discrete time evolution defined by neighbourhood rules. They are used to simulate many complex systems in physics and science in general. In this work,…

Based on a group theoretical setting a sort of discrete dynamical system is constructed and applied to a combinatorial dynamical system defined on the set of certain Bethe ansatz related objects known as the rigged configurations. This…

We extend Cellular Automata to time-varying discrete geometries. In other words we formalize, and prove theorems about, the intuitive idea of a discrete manifold which evolves in time, subject to two natural constraints: the evolution does…