https://github.com/tkf/lyapunovexponents.jl

A hackable Lyapunov exponents calculator
https://github.com/tkf/lyapunovexponents.jl

Last synced: 9 months ago
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A hackable Lyapunov exponents calculator

• Host: GitHub
• URL: https://github.com/tkf/lyapunovexponents.jl
• Owner: tkf
• License: other
• Created: 2018-01-21T02:39:28.000Z (almost 8 years ago)
• Default Branch: master
• Last Pushed: 2020-02-08T15:47:14.000Z (almost 6 years ago)
• Last Synced: 2024-10-19T17:46:26.999Z (over 1 year ago)
• Language: Julia
• Homepage: https://tkf.github.io/LyapunovExponents.jl/latest/
• Size: 7.89 MB
• Stars: 13
• Watchers: 3
• Forks: 5
• Open Issues: 3
• Metadata Files:
  • Readme: README.md
  • License: LICENSE.md

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README

          
# LyapunovExponents.jl --- A hackable Lyapunov exponents calculator

[![Build Status](https://travis-ci.org/tkf/LyapunovExponents.jl.svg?branch=master)](https://travis-ci.org/tkf/LyapunovExponents.jl)

[![Coverage Status](https://coveralls.io/repos/tkf/LyapunovExponents.jl/badge.svg?branch=master&service=github)](https://coveralls.io/github/tkf/LyapunovExponents.jl?branch=master)

[![codecov.io](http://codecov.io/github/tkf/LyapunovExponents.jl/coverage.svg?branch=master)](http://codecov.io/github/tkf/LyapunovExponents.jl?branch=master)

[![](https://img.shields.io/badge/docs-stable-blue.svg)](https://tkf.github.io/LyapunovExponents.jl/stable)

[![](https://img.shields.io/badge/docs-latest-blue.svg)](https://tkf.github.io/LyapunovExponents.jl/latest)

The aim of LyapunovExponents.jl is to provide an efficient research

platform for computations related to Lyapunov exponents.  This is

(planned to be) achieved by exposing low-level APIs to Lyapunov

exponents calculation.

At the moment, LyapunovExponents.jl is still at the very early stage

of development and nowhere close to providing a stable API.

## Features

Implemented:

* Lyapunov exponents calculation based on QR decomposition.

* Maximum Lyapunov exponent calculation.

* [Covariant Lyapunov vectors calculation][CLV example].

* Tangent space evolution based on the automatic differentiation tool

  [ForwardDiff.jl].

* Testing utilities for tangent space evolution (Jacobian calculation)

  provided by users.

* Continuous dynamical systems support based on [DifferentialEquations.jl].

  This means that [the rich set of ODE solvers](http://docs.juliadiffeq.org/latest/solvers/ode_solve.html)

  can be used.

* [Random ordinary differential equation][RODE] support.

* [Various examples of continuous and discrete dynamical systems.][Examples]

* [OnlineStats.jl] support: on-the-fly calculation of Lyapunov

  exponents, their variance, covariance, and any other statics it

  supports.

* (Experimental) Automatic termination.

Wanted list:

* Delay differential equations.

* Partial differential equations.

* Stochastic dynamical systems.

* Poincaré map.

[Examples]: https://tkf.github.io/LyapunovExponents.jl/latest/examples/

[CLV example]: https://tkf.github.io/LyapunovExponents.jl/latest/gallery/Ginelli_2007_Figure_1a/

[DifferentialEquations.jl]: http://juliadiffeq.org

[RODE]: http://docs.juliadiffeq.org/latest/types/rode_types.html

[ForwardDiff.jl]: http://www.juliadiff.org/ForwardDiff.jl

[ChaosTools.jl]: https://juliadynamics.github.io/DynamicalSystems.jl/latest/chaos/overview/

[DynamicalSystems.jl]: https://juliadynamics.github.io/DynamicalSystems.jl/latest/

[OnlineStats.jl]: https://github.com/joshday/OnlineStats.jl

[eom]: https://github.com/termoshtt/eom

## Related works

* [ChaosTools.jl] from the [DynamicalSystems.jl] ecosystem is another

  Julia library which provides easy-to-use, clearly written,

  well-tested, and well-documented Lyapunov exponents calculation.

* [eom] is a Rust library which provides Lyapunov exponents and

  Covariant Lyapunov vectors calculation, on top of configurable

  ODE/PDE solvers.

* (I'm sure there are more...)

## License

The LyapunovExponents.jl package is licensed under the MIT "Expat" License.

See [LICENSE.md]() file.