366 research outputs found
Predictability: a way to characterize Complexity
Different aspects of the predictability problem in dynamical systems are
reviewed. The deep relation among Lyapunov exponents, Kolmogorov-Sinai entropy,
Shannon entropy and algorithmic complexity is discussed. In particular, we
emphasize how a characterization of the unpredictability of a system gives a
measure of its complexity. Adopting this point of view, we review some
developments in the characterization of the predictability of systems showing
different kind of complexity: from low-dimensional systems to high-dimensional
ones with spatio-temporal chaos and to fully developed turbulence. A special
attention is devoted to finite-time and finite-resolution effects on
predictability, which can be accounted with suitable generalization of the
standard indicators. The problems involved in systems with intrinsic randomness
is discussed, with emphasis on the important problems of distinguishing chaos
from noise and of modeling the system. The characterization of irregular
behavior in systems with discrete phase space is also considered.Comment: 142 Latex pgs. 41 included eps figures, submitted to Physics Reports.
Related information at this http://axtnt2.phys.uniroma1.i
Automatic Filters for the Detection of Coherent Structure in Spatiotemporal Systems
Most current methods for identifying coherent structures in
spatially-extended systems rely on prior information about the form which those
structures take. Here we present two new approaches to automatically filter the
changing configurations of spatial dynamical systems and extract coherent
structures. One, local sensitivity filtering, is a modification of the local
Lyapunov exponent approach suitable to cellular automata and other discrete
spatial systems. The other, local statistical complexity filtering, calculates
the amount of information needed for optimal prediction of the system's
behavior in the vicinity of a given point. By examining the changing
spatiotemporal distributions of these quantities, we can find the coherent
structures in a variety of pattern-forming cellular automata, without needing
to guess or postulate the form of that structure. We apply both filters to
elementary and cyclical cellular automata (ECA and CCA) and find that they
readily identify particles, domains and other more complicated structures. We
compare the results from ECA with earlier ones based upon the theory of formal
languages, and the results from CCA with a more traditional approach based on
an order parameter and free energy. While sensitivity and statistical
complexity are equally adept at uncovering structure, they are based on
different system properties (dynamical and probabilistic, respectively), and
provide complementary information.Comment: 16 pages, 21 figures. Figures considerably compressed to fit arxiv
requirements; write first author for higher-resolution version
Synchronization of non-chaotic dynamical systems
A synchronization mechanism driven by annealed noise is studied for two
replicas of a coupled-map lattice which exhibits stable chaos (SC), i.e.
irregular behavior despite a negative Lyapunov spectrum. We show that the
observed synchronization transition, on changing the strength of the stochastic
coupling between replicas, belongs to the directed percolation universality
class. This result is consistent with the behavior of chaotic deterministic
cellular automata (DCA), supporting the equivalence Ansatz between SC models
and DCA. The coupling threshold above which the two system replicas synchronize
is strictly related to the propagation velocity of perturbations in the system.Comment: 16 pages + 12 figures, new and extended versio
Formal Definitions of Unbounded Evolution and Innovation Reveal Universal Mechanisms for Open-Ended Evolution in Dynamical Systems
Open-ended evolution (OEE) is relevant to a variety of biological, artificial
and technological systems, but has been challenging to reproduce in silico.
Most theoretical efforts focus on key aspects of open-ended evolution as it
appears in biology. We recast the problem as a more general one in dynamical
systems theory, providing simple criteria for open-ended evolution based on two
hallmark features: unbounded evolution and innovation. We define unbounded
evolution as patterns that are non-repeating within the expected Poincare
recurrence time of an equivalent isolated system, and innovation as
trajectories not observed in isolated systems. As a case study, we implement
novel variants of cellular automata (CA) in which the update rules are allowed
to vary with time in three alternative ways. Each is capable of generating
conditions for open-ended evolution, but vary in their ability to do so. We
find that state-dependent dynamics, widely regarded as a hallmark of life,
statistically out-performs other candidate mechanisms, and is the only
mechanism to produce open-ended evolution in a scalable manner, essential to
the notion of ongoing evolution. This analysis suggests a new framework for
unifying mechanisms for generating OEE with features distinctive to life and
its artifacts, with broad applicability to biological and artificial systems.Comment: Main document: 17 pages, Supplement: 21 pages Presented at OEE2: The
Second Workshop on Open-Ended Evolution, 15th International Conference on the
Synthesis and Simulation of Living Systems (ALIFE XV), Canc\'un, Mexico, 4-8
July 2016 (http://www.tim-taylor.com/oee2/
An evolutionary approach to the identification of Cellular Automata based on partial observations
In this paper we consider the identification problem of Cellular Automata
(CAs). The problem is defined and solved in the context of partial observations
with time gaps of unknown length, i.e. pre-recorded, partial configurations of
the system at certain, unknown time steps. A solution method based on a
modified variant of a Genetic Algorithm (GA) is proposed and illustrated with
brief experimental results.Comment: IEEE CEC 201
Identification of cellular automata based on incomplete observations with bounded time gaps
In this paper, the problem of identifying the cellular automata (CAs) is considered. We frame and solve this problem in the context of incomplete observations, i.e., prerecorded, incomplete configurations of the system at certain, and unknown time stamps. We consider 1-D, deterministic, two-state CAs only. An identification method based on a genetic algorithm with individuals of variable length is proposed. The experimental results show that the proposed method is highly effective. In addition, connections between the dynamical properties of CAs (Lyapunov exponents and behavioral classes) and the performance of the identification algorithm are established and analyzed
The Stabilizing Effect of Noise on the Dynamics of a Boolean Network
In this paper, we explore both numerically and analytically the robustness of a synchronous Boolean network governed by rule 126 of cellular automata. In particular, we explore whether or not the introduction of noise into the system has any discernable effect on the evolution of the system. This noise is introduced by changing the states of a given number of nodes in the system according to certain rules. New mathematical models are developed for this purpose. We use MATLAB to run the numerical simulations including iterations of the real system and the model, computation of Lyapunov exponents, and generation of bifurcation diagrams. We provide a more in-depth fixed-point analysis through analytic computations paired with a focus on bifurcations and delay plots to identify the possible attractors. We show that it is possible either to attenuate or to suppress entirely chaos through the introduction of noise and that the perturbed system may exhibit very different long-term behavior than that of the unperturbed system
- …