DynamicalSystems.jl - news, updates, and announcements

Specific Domains Modelling & Simulations
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Hello everyone,

this Topic will serve as a “mega-thread” sorts of post where all updates regarding the DynamicalSystems.jl library are posted. The updates here will range from noteworthy new features to potentially breaking changes in the ecosystem.

We are moving away from posting updates in the REPL (what we did in the past), and we will be using this post instead for improved user experience. If a user wants to follow updates, they can “subscribe” to this particular post at a notification level they deem desirable!

please consider not posting any replies on this Topic to not notify users unnecessarily. Rather, create new Topics if you have aspects of the library to discuss, in particular for troubleshooting

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And what best way to start the news but with the brand new, ultra-super-duper cool logo for DynamicalSystems.jl:

https://github.com/JuliaDynamics/JuliaDynamics/blob/master/videos/dynamicalsystems/juliadynamics_logo_anim_dark.gif?raw=true(image larger than 4 MB)

which is available in all sorts of dark / light / transparent variants:

DynamicalSystems.jl logo: The Double Pendulum
DynamicalSystems.jl logo: The Double Pendulum6400×2400 728 KB

DynamicalSystems.jl logo: The Double Pendulum
DynamicalSystems.jl logo: The Double Pendulum6400×2400 694 KB

(what a cool slowdown oh my god)

You can find all logo-related resources here:

(MIT licensed go nuts you can post them wherever you want)

and the script that generated the logo is:

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Another update concerns the StateSpaceSets.jl subpackage of the library that deals with sets in the state space. It was recently updated to v2, with the breaking change that now StateSpaceSet <: AbstractVector{<:AbstractVector}. Normally this should only affect developers that were using the type of StateSpaceSet, but do go ahead and report any breakage in code. It is unlikely as we tested the change extensively, but one can never truly know… :slight_smile:

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A fantastic new feature was merged recently in Attractors.jl: the (AttractorSeedContinueMatch)[API · Attractors.jl] global continuation method. This method is arguably the crown jewel of Attractors.jl as it is a cutting edge method in continuation in dynamical systems and it entirely modular: it can be composed by any method of finding attractors and any method of matching attractors.

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Jacobians in DynamicalSystems.jl will now re-use symbolic Jacobians created by ModelingToolkit, if the system was generated with from an MTK model.

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Oh boy I haven’t posted here in a while despite the large amount of new features that are constantly entering DynamicalSystems.jl! So I’ll write now from the top of my head a bunch of new stuff:

  • PeriodicOrbits.jl is a new package that is part of DynamicalSystrems.jl.
  • SignalDecomposition.jl and TransitionsInTimeseries.jl are now also part of the package.
  • A fantastic brand new feature resulting from brand new research has been merged into Attractors.jl: StabilityMeasuresAccumulator that calculate various measures of stability for dynamical systems along a global continuation
  • Now StateSpaceSets can have named dimensions. There is some automation with MTK generated dynamical systems: functions like trajectory and the attractor finding of Attractors.jl will automatically name the generated StateSpaceSets with the named dimensions of the dynamical system (whose names are the named variables of the MTK system)
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Ah, it’s been too long since the last post here, and there have been too many things merged into DynamicalSystems.jl! Here’s a list of highlights from my recent memory!

  • RecurrenceMicrostatesAnalysis.jl is a new package that has joined DynamicalSystems.jl
  • New quantity for analysing basins of attraction, called intermingledness, is now in Attractors.jl. We also published an arXiv paper applying it to high dimensional climate data: [2604.09661] Multistability and intermingledness in complex high-dimensional data
  • The TransferOperator of ComplexityMeasures.jl has just been substantially improved and extended to be applicable to any counting based outcome space
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Sticking in the plan of posting more regular updates here, this is a big one! Next August (2027), it will be the 10 years anniversary of DynamicalSystems.jl! I am putting together a Symposium (miniconference) to celebrate this! Please join!

Details are here: JuliaDynamics + DynamicalSystems.jl 10 year Symposium

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In other big news, Attractors.jl v2 has been released. This release comes with lots of new features and a massive renaming of the APIs, so please see the CHANGELOG.md for all details. This release also accompanies our paper on global continuation, I technique I believe is genuinely a true breakthrough in dynamical systems! You can find the paper here: [2607.09332] Global continuation as a complement to traditional continuation and bifurcation analysis !

and p.s.; remember to register your interest in the 10 years anniversary symposium of the post above!

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Could you summarize the breakthrough for us?

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I’d prefer to keep this thread clean regarding discussions, focusing on announcements only for DynamicalSystems.jl, so that users can subscribe via email to this thread. I will provide here the abstract excerpt that I think highlights the uniqueness of the method, and happy to answer more in DMs:

To address some inherent challenges of
local continuation and to provide fundamentally new infor-
mation during a continuation, this paper introduces global
continuation as a complement suitable for the study of
multistability, critical transitions and real-world-oriented
applications. Global continuation finds and continues in
parallel (practically) all system attractors and their re-
sponse to finite perturbations by synthesising information
from the whole state space, while placing a focus on the
qualities or observables of a dynamical system that the
practitioner cares about in context. Global continuation
does not require deep expertise and is effortless to use
and troubleshoot, making it attractive to applied scientists
from different disciplines.

also, in my judgement, global continuation is the first time a truly different and generic continuation technique is published; the established quo is additions to the existing technique of local continuation while keeping the core idea the same.

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Thanks for summarizing the approach.