DynamicalSystems.jl logo: The Double Pendulum

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DynamicalSystems.jl is an award-winning Julia software library for nonlinear dynamics and nonlinear timeseries analysis.

To install DynamicalSystems.jl, run import Pkg; Pkg.add("DynamicalSystems") as a Julia language command. To learn how to use it and see its contents visit the documentation, which you can either find online or build locally by running the docs/make.jl file.

DynamicalSystems.jl is part of JuliaDynamics, an organization dedicated to creating high quality scientific software.


Aspects of DynamicalSystems.jl that make it stand out among other codebases for nonlinear dynamics or nonlinear timeseries analysis are:

  • Exceptional documentation. All implemented algorithms provide a high-level scientific description of their functionality in their documentation string as well as references to scientific papers. The documentation features hundreds of tutorials and examples ranging from introductory to expert usage.
  • Accessible source code. One of the main priorities of the library is that the source code of (almost) all implementations is small, simple, easy to understand and modify. This increases confidence, reduces bugs, and allows users to become developers without unnecessary effort.
  • Open source community project. Built from the ground up entirely on GitHub, DynamicalSystems.jl is 100% open source and based on community contributions. Anyone can be a developer of the library. Everyone is welcomed.
  • Extensive content. It aims to cover the entire field of nonlinear dynamics and nonlinear timeseries analysis. It has functionality for complexity measures, delay embeddings, periodic orbits, nonlocal stability analysis, continuation, chaos, fractal dimensions, surrogate testing, recurrence quantification analysis, and much more. Furthermore, all algorithms are "general" and work for any dynamical system applicable. Missing functionality that falls under this wide category of content is welcomed to be part of the library!
  • Well tested. All implemented functionality is extensively tested. Each time any change in the code base is done, the extensive test suite is run and checked before merging the change in.
  • Extendable. DynamicalSystems.jl is a living, evolving project. New contributions can become part of the library and be accessed by all users in the next release. Most importantly, all parts of the library follow professional standards in software design and implement extendable interfaces so that it is easy to contribute new functionality.
  • Active development. Since the start of the project (May 2017) there has been activity every month: new features, bugfixes, and the developer team answers users questions on official Julia language forums.
  • Performant. Written entirely in Julia, heavily optimized and parallelized, and taking advantage of some of the best packages within the language, DynamicalSystems.jl is really fast.


The DynamicalSystems.jl library started as a vision with three main goals; These same goals now are the core pillars guiding development, and are largely the source of where the aforementioned unique highlights stem from.

Goal 1: Accessible and reproducible nonlinear dynamics

The first goal of the library is to make this beautiful field accessible and reproducible.

Accessible means that if you read on some sorts of fancy algorithm online in a scientific article, you should be able to use it instantly. You shouldn't have to put in the work to code it yourself. The authors of the paper already did that. So why should you do it again?! To resolve this problem we developed, and continue to develop, a library that has an incredibly low threshold of entry: contributing to DynamicalSystems.jl and making your code available to all is truly easier than coding your own algorithms from scratch, due to the well thought out and generic interfaces it provides for dynamical systems.

Reproducible means that given some sorts of dynamical systems analysis in a scientific article, you should be able to do exactly the same analysis and get exactly the same results (within some numeric precision) as the article. After all, computers are deterministic constructs. DynamicalSystems.jl allows this by (1) being written in a modern programming language with incredible environment and reproducibility support, (2) being well tested, and (3) by providing thousands of algorithms out of the box, allowing most dynamical systems analysis to be done instantly while implementing only as little new stuff as necessary.

Goal 2: Library in the literal sense

DynamicalSystems.jl is not just a software library. It is also a library in the literal sense: where people go to learn something new (here in particular for nonlinear dynamics). That is why the documentation is of exceptionally high quality: detailed descriptions and explanations of algorithms, with references to the scientific articles articles. It is also partly a reason for the source code to be written as clearly as possible, so that it is examinable by any user.

Goal 3: A general purpose software

The third goal is to fill the missing gap of a high quality general purpose software for nonlinear dynamics which can be easily extended with new functionality. This can be particularly impactful in teaching. You see, it is unfortunately rarely the case that real, runnable code is shown in the classroom, because it is often long and messy. This is especially hurtful for nonlinear dynamics, a field where computer-assisted exploration is critical.

DynamicalSystems.jl provides teachers with a framework capable of demonstrating actual, real-world nonlinear dynamics code and its output, without having to invest the weeks to code the internal infrastructure themselves. Its high level syntax requires writing little code to get lots of meaningful analysis done, while its extensive functionality covers most typical classroom applications.