Skip to content

Features Overview

The features offered in this documentation section come from the package ChaosTools.jl. If you are encountering an issue with some of the methods, you can report/open a new issue at the GitHub Issues page.

Orbit Diagrams

  1. Orbit diagrams (aka bifurcation diagrams) of maps: orbitdiagram.
  2. Poincaré surfaces of section for continuous systems: poincaresos.
  3. Automated production of orbit diagrams for continuous systems: produce_orbitdiagram.

Lyapunov Exponents

The following treat systems where the equations of motion are known:

  1. Maximum Lyapunov exponent for both discrete and continuous systems: lyapunov.
  2. Lyapunov spectrum for both discrete and continuous systems: lyapunovs.

Categorizing Chaos

  1. The Generalized Alignment Index: \text{GALI}_k : gali.

    • Implemented for both discrete and continuous systems.

    • A test to categorize strong chaos, partially predictable chaos and regular behavior: predictability.

    • Implemented for both discrete and continuous systems.

Entropies and Dimensions

  1. Generalized (Renyi) entropy: genentropy.
  2. Permutation entropy: permentropy.
  3. Fast and cheap (memory-wise) method for computing entropies of large datasets.
  4. Generalized dimensions (e.g. capacity dimension, information dimension, etc.): generalized_dim.
  5. Kaplan-Yorke dimension: kaplanyorke_dim.
  6. Automated detection of best algorithmic parameters for calculating attractor dimensions.

And, in order to automatically deduce dimensions, we also offer methods for:

  • Partitioning a function y(x) vs. x into regions where it is approximated by a straight line, using a flexible algorithm with a lot of control over the outcome. See linear_regions.
  • Detection of largest linear region of a function y(x) vs. x and extraction of the slope of this region.

Nonlinear Timeseries Analysis

  1. Broomhead-King coordinates: broomhead_king.
  2. Numerically determining the maximum Lyapunov exponent of a (e.g. experimentally) measured timeseries: numericallyapunov.

Periodicity

  1. Numerical method to find unstable and stable fixed points of any ordern of a discrete map (of any dimensionality): periodicorbits.

    • Convenience functions for defining and realizing all possible combinations of \mathbf{\Lambda}_k matrices required in the above method.