Introduction

DynamicalSystems.jl is a Julia suite for the exploration of chaos and nonlinear dynamics.

You can join our chatroom for discussions related to dynamical systems and Julia as well as for asking questions about the packages of the JuliaDynamics organization!

Be sure to visit the Contributor Guide page, because you can help make this package better without having to write a single line of code! Also, if you find this package helpful please consider staring it on GitHub! This gives us an accurate lower bound of users that this package has already helped!

Our Goals

Our aim is for the DynamicalSystems.jl ecosystem to be a useful and powerful companion for students and scientists working on chaos and nonlinear dynamics.

One of a major goals of this ecosystem is to be completely transparent as to what is going on "under the hood". In scientific research, you never want to use black boxes, e.g. functions that give a result without telling you how it was calculated. DynamicalSystems.jl battles this in 3 ways:

1. It is written entirely in Julia, making the source code clear and easy to understand for even novice users.
2. Almost every documentation string gives direct references to the original papers where the algorithm is taken from, in case some users don't understand (or simply don't want to read) the source code. For example, the documentation string of lyapunovs will cite relevant publications for the definition and computation of the lyapunov spectrum.
3. Documentation strings for exported names have summarized descriptions of the algorithms (whenever it is possible).

Another major goal is to offer code that is concise, intuitive, performant and general. All functions work just as well with anyDynamicalSystem, whether it is a simple continuous chaotic system, like the Lorenz attractor, or a high dimensional discrete map like 20 coupled standard maps!

For example, provided you have first defined a DynamicalSystem (which simply reduces to writing a function for the equations of motion), you should be able to e.g. calculate the Lyapunov spectrum for it in a single line:

lyapunovs(system, times_to_do_QR; keywords...)

The same function call works with any system, no discriminations here!

Installation

Simply use Pkg.add("DynamicalSystems") to install everything.

We highly suggest our users to read the The latest documentation and not the stable one. The reasoning is simple: the repository of DynamicalSystems is a package coordinator and documentation host for the DynamicalSystems.jl ecosystem. It will often be that a new tag will exist for one of the packages of the ecosystem but not for the repository of DynamicalSystems itself. Thus you can only read the documentation of the latest features by visiting the latest documentation version.

Notice however, that this does not have anything to do with the official release versions of packages that do contain the actual code. Because our documentation is based on utilizing Documenter.jl and the documentation strings of exported function names, you can be assured that the documentation you read on the latest page reflects accurately the latest release versions.

Low Dependency usage

All packages of the DynamicalSystems.jl ecosystem have a dependency on DynamicalSystemsBase.jl. By running Pkg.add("DynamicalSystems") you install all the packages of the ecosystem. That is not necessary however, since DynamicalSystems.jl is a bridging package that exports everything and hosts the documentation.

For example, if you only need the features of ChaosTools.jl then you can get away by doing only Pkg.add("ChaosTools") and all other dependencies will be resolved accordingly.

Contents

DynamicalSystemsBase.jl

1. Intuitive, consistent APIs for the definition of general dynamical systems.
2. Discrete Maps
3. Continuous Flows
4. Dedicated interface for Numerical Data
5. Automatic "completion" of the dynamics of the system with numerically computed Jacobians, in case they are not provided by the user.
6. Well-defined functions for (numerically) evolving dynamical systems.
7. Library of predefined well-known dynamical systems that have been used extensively in scientific research.

ChaosTools.jl

Please see the overview section for a full list of features.

Quick summary:

• Lyapunov Exponents
• Entropies and Dimensions
• Delay Coordinates Embedding
• Neighborhood estimation
• Lyapunov exponent of a timeseries
• Finding Fixed Points of any Map of any order
• Detecting Chaos

Wanted Features

The wanted features GitHub page lists features that are wanted by the DynamicalSystems.jl ecosystem and are open to contributors.