Symbolic Dynamics, Coarse Graining and the Monitoring of Complex Systems

  title={Symbolic Dynamics, Coarse Graining and the Monitoring of Complex Systems},
  author={Vasileios Basios and D{\'o}nal Mac Kernan},
  journal={Int. J. Bifurc. Chaos},
Coarse graining techniques and their associated symbolic dynamics are reviewed with a focus on probabilistic aspects of complex dynamical systems. The probabilistic approach initiated by Nicolis and coworkers has been elaborated. One of the major issues when dealing with the dynamics of complex nonlinear systems, the fact that the inherent time-scales of the unfolding phenomena are not well separated, is brought into focus. Recent results related to this interdependence, which is one of the… 

Figures from this paper

Measuring chaos in the Lorenz and Rössler models: Fidelity tests for reservoir computing.

This study considers two famous systems, Lorenz and Rössler models with their iconic attractors, and demonstrates that with adequately chosen symbolic partition, three measures of complexity work remarkably well for characterizing the degree of chaoticity and precise detecting stability windows in the parameter space.

Chaotic dynamics in biological information processing: Revisiting and revealing its logic (a mini-review).

It is demonstrated, by utilizing a minimal model for apprehension and judgement related to Bayesian updating, that the fundamental characteristics of a biological processor obey an extended, non-Boolean, logic which is characterized as a quantum logic.

Symbolic dynamics of music from Europe and Japan.

It is observed that the departure of "total randomness" to the constraints underlying the dynamics of the symbol generating process can be accurately assessed by the texts' block-entropy vs block-length scaling laws.

Estimating Permutation Entropy Variability via Surrogate Time Series

This paper proposes a method to overcome the difficulty of assessing, out of a single time series, not only the PE value, but also its uncertainty by using generation of surrogate time series.

C D ] 1 4 O ct 2 01 8 Symbolic Dynamics of Music from Europe and Japan

It is observed that the departure of “total randomness” to the constrains underlying the dynamics of the symbol generating process can be accurately assessed by the texts’ block-entropy versus block-length scaling laws.



Dynamical Aspects of Interaction Networks

A connection between dynamical systems and network theory is outlined based on a mapping of the dynamics into a discrete probabilistic process, whereby the phase space is partitioned into finite size

Symbolic Dynamics Generated by a Combination of Graphs

This paper investigates the growth rate of the number of all possible paths in graphs with respect to their length in an exact analytical way and identifies conditions for a stretched exponential type of growth.

Recurrence time statistics in deterministic and stochastic dynamical systems in continuous time: a comparison

The dynamics of transitions between the cells of a finite phase-space partition is analyzed for deterministic and stochastic dynamical systems in continuous time. Special emphasis is placed on the

Foundations Of Complex Systems: Nonlinear Dynamics, Statistical Physics, Information And Prediction

The Phenomenology of Complex Systems Quantitative View and Communicating with a Complex System: Monitoring, Analysis and Prediction Selected Topics.

Markov processes, dynamic entropies and the statistical prediction of mesoscale weather regimes

The data pertaining to transitions between weather regimes grouped in 3 clusters are analyzed. Evidence that the dynamics of transitions between the regimes is not a first order Markov process is

Dynamics of fine scale variables versus averaged observables in a simplified thermal convection model

The dynamical properties of time- and space-averaged observables of a simplified one-dimensional thermal convection model are explored and compared to those of the fine scale variables. It is found

Super-selection rules modulating complexity: an overview

An Introduction to Symbolic Dynamics and Coding

Requiring only a undergraduate knowledge of linear algebra, this first general textbook includes over 500 exercises that explore symbolic dynamics as a method to study general dynamical systems.