Hello everyone!
In this post I’m happy to announce the latest news surrounding the DynamicalSystems.jl library! In the following I’ll summarize the most exciting things that have been happening to the library over the previous year(s). Most of these have been incrementally added over time and are not really strictly part of 2.0 release, but oh well.
Typically this post would have been a blog post, but actually I don’t have a blog so here we are!
A main conclusion I can draw from all these updates is that according to my knowledge, more than 80% of the DynamicalSystems.jl functionality does not exist in any other open source package for any language. (please do let me know if you think I’m wrong, I would be very happy to encounter competition!)
Nonlinear dynamics textbook
Over the last two years we’ve been working on a new way to teach nonlinear dynamics. This cultivated into a new physics/mathematics textbook that explicitly includes runnable Julia code snippets and will soon be published in Springer’s “Undergraduate Lecture Notes in Physics” series.
My JuliaCon2021 talk Changing Physics education with Julia talks about the book in detail, so I’ll refer there! There is also an online repo related with the book: GitHub - JuliaDynamics/NonlinearDynamicsTextbook: Nonlinear Dynamics: A concise introduction interlaced with code
Small breaking changes
Two small breaking changes have occurred in this release:
-
Keyword argument
dtwas clashing withdtfrom DifferentialEquations.jl and had to be renamed. It is now namedΔt, accessed with\Delta<TAB>t. Many functions have been affected by this, e.g.lyapunov, lyapunovspectrum, gali, expansionentropy, orbitdiagram. -
Datasetindexing has been clarified with a minor breaking change thatdataset[i::AbstractVector]now returning aDatasetinstead of aVector{SVector}. -
All deprecations existing in previous versions have been removed.
-
Some new deprecations have been added, which rename things for greater clarity.
Delay embeddings
We have moved forwards to a generalized embedding interface (genembed). This interface not only clears previously clunky structs, but allows some advanced methods of nonlinear dynamics (see below) to be implemented in an intuitive manner.
We now have implemented many, many new methods for delay coordinates embeddings.
We have an automated method for optimal embedding via the traditional approach.
We have also implemented the new cutting edge research on delay embedding, following the so called unified approach. A paper we wrote on a new method can be found here: A unified and automated approach to attractor reconstruction - IOPscience
All this huge amount of work is due to @hkraemer (Hauke Kraemer)!
Entropies.jl
“New” Julia package from main author @kahaaga (Kristian A. Haaga) which is also part of the DynamicalSystems.jl library! It provides an interface to obtain probability distributions representing trajectories or sets in the state space. These probabilities can then be used to calculate a corresponding entropy. At the moment we have at least a dozen of distinct estimators.
Fractal dimensions
With the hard work of @apbraun (Anton Braun) and @igkottlarz (Inga Kottlarz), we have implemented several methods to estimate fractal dimensions. We used these methods to compare fractal dimension estimates in a thorough manner, something that was missing from the nonlinear dynamics literature. A paper with this comparison will be soon available on arXiv.
link to paper pending, subscribe to this post to get an update
Basins of attraction
Huge contributions from @awage (Alexandre Wagemakers) provided quality algorithms for finding basins of attraction of dynamical systems and to estimate the fractal nature of basin boundaries. We have a brand new basin method basins_of_attraction which works for any dynamical system: discrete, continuous, Poincare map, stroboscopic map, high dimensional, lower-dimensional projections of higher-dimensional, you name it.
It does not exist anywhere else and we are currently writing a paper about it that we will soon put on arXiv.
link to paper pending, subscribe to this post to get an update
Tipping points
The basins of attraction contributions opened the door for DynamicalSystems.jl to start implementing algorithms and concepts related to Tipping Points, which are the fanciest things happening on dynamical systems research in the past couple of years, and it is of major relevance for climate change. In fact, most conferences with anything related to climate will probably have a session on tipping points, and now I can happily say that DynamicalSystems.jl is having such methods!
(Unfortunately, even to this day, papers published in 2020 still do not make their methods available as open source implementations. I implement as much as I can to DynamicalSystems.jl after reading the papers, but I still long for the day where each published paper will have code published with it…)
Miscellaneous additions
There have been several miscellaneous additions, e.g. mean_return_times in ChaosTools.jl, and Recurrence Networks in RecurrenceAnalysis.jl. It is best to see the Contents page of the docs for more!
Colorblind-friendly color palette
In the spirit of inclusivity I wanted to come up with a colorblind friendly palette to use in the book and as well in the documentation of JuliaDynamics packages. Thankfully, with the help of this amazing website by David Nichols I was able to come up with the following palette:
(p.s. i love purple)
COLORSCHEME = [
"#6F4AC7",
"#33CBD8",
"#1B1B1B",
"#E82727",
"#535D7F",
"#A6D210",
]
So in this subsection I pretty much wanted to advertise the website by David Nichols 
Thank you
Thanks to everyone that contributed to the library so far! You can see all of them here: JuliaDynamics
And thank you all for taking the time to read this update, and for supporting this library in any conceivable manner. Every single star on GitHub, or every single mentioning of the library, I can see it, and I appreciate every single one tremendously!
Is there any information yet?