Related papers: Measuring Complexity in Cantor Dynamics
We evaluate new complexity measures on the symbolic dynamics of coupled tent maps and cellular automata. These measures quantify complexity in terms of $k$-th order statistical dependencies that cannot be reduced to interactions between…
A measure of complexity based on a probabilistic description of physical systems is proposed. This measure incorporates the main features of the intuitive notion of such a magnitude. It can be applied to many physical situations and to…
We recall the definition of the $\epsilon$-distortion complexity of a set defined in \cite{bcc} and the results obtained in this paper for Cantor sets of the interval defined by iterated function systems. We state an analogous definition…
We propose a metric to characterize the complex behavior of a dynamical system and to distinguish between organized and disorganized complexity. The approach combines two quantities that separately assess the degree of unpredictability of…
We describe the approximation of a continuous dynamical system on a p. l. manifold or Cantor set by a tractable system. A system is tractable when it has a finite number of chain components and, with respect to a given full background…
We propose a new way to measure the balance between freedom and coherence in a dynamical system and a new measure of its internal variability. Based on the concept of entropy and ideas from neuroscience and information theory, we define…
In a topological dynamical system the complexity of an orbit is a measure of the amount of information (algorithmic information content) that is necessary to describe the orbit. This indicator is invariant up to topological conjugation. We…
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 define {\em semantic complexity} using a new concept of {\em meaning automata}. We measure the semantic complexity of understanding of prepositional phrases, of an "in depth understanding system", and of a natural language interface to…
While the notion of chaos is well established for dynamical systems on manifolds, it is not so for dynamical systems over discrete spaces with $ N $ variables, as binary neural networks and cellular automata. The main difficulty is the…
This paper draws distinctions among various concepts related to tipping points, robustness, path dependence, and other properties of system dynamics. For each concept a formal definition is provided that utilizes Markov model…
Complexity is a multi-faceted phenomenon, involving a variety of features including disorder, nonlinearity, and self-organisation. We use a recently developed rigorous framework for complexity to understand measures of complexity. We…
Complex systems have become a popular lens for analyzing cities and complexity theory has many implications for urban performance and resilience. This paper develops a typology of measures and indicators for assessing the physical…
We discuss some aspects of the extension to continuous systems of a statistical measure of complexity introduced by Lopez-Ruiz, Mancini and Calbet (LMC) [Phys. Lett. A 209 (1995) 321]. In general, the extension of a magnitude from the…
The definition of complexity through Statistical Complexity Measures (SCM) has recently seen major improvements. Mostly, effort is concentrated in measures on time series. We propose a SCM definition for spatial dynamical systems. Our…
The (e,n)-complexity functions describe total instability of trajectories in dynamical systems. They reflect an ability of trajectories going through a Borel set to diverge on the distance $\epsilon$ during the time interval n. Behavior of…
We study dynamical systems using measures taking values in a non-Archimedean field. The underlying space for such measure is a zero-dimensional topological space. In this paper we elaborate on the natural translation of several notions,…
We study correlation measures for complex systems. First, we investigate some recently proposed measures based on information geometry. We show that these measures can increase under local transformations as well as under discarding…
Data complexity is an important concept in the natural sciences and related areas, but lacks a rigorous and computable definition. In this paper, we focus on a particular sense of complexity that is high if the data is structured in a way…
Using the combinatorial properties of subsets of integers, a classification of metric dynamical systems was given in [V. Bergelson and T. Downarowicz, Large sets of integers and hierarchy of mixing properties of measure-preserving systems,…