#dynamicalsystems

We finish the sixth day of the Konstanz School of Collective Behaviour 2025 (#KSCB2025) with a #tutorial by Marco Fele on #modelling #DecisionMaking in #DynamicalSystems

@cbehav.bsky.social

https://www.exc.uni-konstanz.de/kscb/

Today, on #ICongressoDoIMECC, Prof. Marco Antonio Teixeira (IMECC/UNICAMP) will present a plenary talk on "Refractive Systems".

"I will briefly and roughly discuss a topic in NSDS (Refractive Systems) that I am currently interested in. We intend to, colloquially discussing some properties of such class of non-smooth dynamical systems (NSDS). In this way, local stability conditions in dimension 3 are discussed. It is worth to say that such subject is still poorly understood in higher dimension."

#Unicamp #IMECC #DynamicalSystems

https://www.youtube.com/live/vHXBEZMS7U0?si=imenA-HAoHCyYRQZ

re-#introduction
Hi Fediscience! I am an Assistant Professor of Mechanical Engineering at University of Hawaiʻi at Mānoa (Honolulu). I got here starting from Physics training with many scientific detours into data-driven models, complex systems, nanomaterial self-assembly, human learning of complex networks, naval ships, and design problems.
I grew up in Belarus and have *opinions* on that region of the world. I've been on Fediverse since late 2022 when *something* happened to our previous cybersocial infrastructure, but the previous server I was on is sunsetting. Please come say hi and recommend cool people to follow here.
I have a blog with longer thoughts on science-adjacent topics.
https://www.aklishin.science/blog/
#ComplexSystems #NetworkScience #DataScience #DynamicalSystems #CollectiveBehavior #StatisticalPhysics

A few days back, I posted some #AnimatedGifs of the exact solution for a large-amplitude undamped, unforced #Pendulum. I then thought to complete the study to include the case when it has been fed enough #energy to allow it just to undergo #FullRotations, rather than just #oscillations. Well, it turns out that it is “a bit more complicated than I first expected” but I finally managed it.

#Mathematics #AppliedMathematics #SpecialFunctions #DynamicalSystems #NonlinearPhenomena

Can time series (TS) #FoundationModels (FM) like Chronos zero-shot generalize to unseen #DynamicalSystems (DS)? #AI

No, they cannot!

But *DynaMix* can, the first TS/DS foundation model based on principles of DS reconstruction, capturing the long-term evolution of out-of-domain DS: https://arxiv.org/pdf/2505.13192v1

Unlike TS foundation models, DynaMix exhibits #ZeroShotLearning of long-term stats of unseen DS, incl. attractor geometry & power spectrum, w/o *any* re-training, just from a context signal.
It does so with only 0.1% of the parameters of Chronos & 10x faster inference times than the closest competitor.

It often even outperforms TS FMs on forecasting diverse empirical time series, like weather, traffic, or medical data, typically used to train TS FMs.
This is surprising, cos DynaMix’ training corpus consists *solely* of simulated limit cycles & chaotic systems, no empirical data at all!

And no, it’s neither based on Transformers nor Mamba – it’s a new type of mixture-of-experts architecture based on the recently introduced AL-RNN (https://proceedings.neurips.cc/paper_files/paper/2024/file/40cf27290cc2bd98a428b567ba25075c-Paper-Conference.pdf), specifically trained for DS reconstruction.

Remarkably, DynaMix not only generalizes zero-shot to novel DS, but it can even generalize to new initial conditions and regions of state space not covered by the in-context information.

We dive a bit into the reasons why current time series FMs not trained for DS reconstruction fail, and conclude that a DS perspective on time series forecasting & models may help to advance the #TimeSeriesAnalysis field.

I'd forgotten what a great concept phase space is! This plot of the state of a pendulum over time is delightful. Play around with it for yourself: openprocessing.org/sketch/1989770 #maths #physics #dynamicalSystems

(10/n) If you’ve made it this far, you’ll definitely want to check out the full paper. Grab your copy here:
https://www.biorxiv.org/content/10.1101/2024.12.17.628339v1
Sharing is highly appreciated!
#compneuro #neuroscience #NeuroAI #dynamicalsystems

Everyone knows about synchronization in chaotic systems. But what happens when one studies the synchronizability of periodic ones? Two main things.

The first is that new classes of synchronization stability emerge that are characteristic of periodic systems and are not found in chaotic ones. The root cause of this is that the master stability function of periodic systems is 0 at the origin, in difference to what happens in chaotic systems, for which it is strictly positive.

The second thing is that we challenge the long-held belief that periodic systems synchronize in a stable way for any coupling, no matter how small. In fact, we show that many of them, for many coupling schemes, have a non-zero lower threshold for synchronization stability.

https://journals.aps.org/prresearch/abstract/10.1103/PhysRevResearch.6.043105

#physics #mathematics #networks #complexsystems #chaos #dynamicalsystems #synchronization #complexity #stability

Symbolic dynamics builds a bridge from #DynamicalSystems to computation/ #AI!

In our #NeurIPS2024 (@NeurIPSConf) paper we present a new network architecture, Almost-Linear RNNs (Fig. 1), that finds most parsimonious piecewise-linear representations of DS from data:
https://arxiv.org/abs/2410.14240

These representations are topologically minimal (Fig. 5,7), profoundly easing interpretation and math. analysis of the underlying data-generating DS.

The AL-RNN furthermore naturally gives rise to a symbolic encoding that provably preserves important topological properties of the underlying dynamical system.
Symbolic dynamics directly links up with computational graphs, finite state machines, formal languages etc. (Fig. 2).

Spearheaded by Manuel Brenner and Christoph Hemmer, jointly with Zahra Monfared.

Interested in interpretable #AI foundation models for #DynamicalSystems reconstruction?

In a new paper we move into this direction, training common latent DSR models with system-specific features on data from multiple different dynamical regimes and DS: https://arxiv.org/pdf/2410.04814
(Fig. 7)

We show applications like transfer & few-shot learning, but most interestingly perhaps, subject/system-specific features were often linearly related to control parameters of the underlying dynamical system trained on …
(Fig. 4)

This gives rise to an interpretable latent feature space, in which datasets with similar dynamics cluster. Intriguingly, this clustering according to *dynamical systems features* led to much better separation of groups than could be achieved by more traditional time series features.
(Fig. 6)

Fantastic work by the incomparable Manuel Brenner and Elias Weber, together with Georgia Koppe!

Yesterday, I posted an image of the #LorenzAttractor showing the evolution of three trajectories (shown in red, green and blue) starting close together. Here, I’ve made it into a little animation to show how the paths initially stay close to each other but after about a quarter of the duration plotted, they #diverge from each other irrevocably (i.e. become uncorrelated) but remain part of the #ChaoticAttractor.

#DynamicalSystems #Mathematics #AppliedMathematics #CCBYSA #FreeSoftware #WxMaxima

Just messing about a bit. Here is the famous #LorenzAttractor plotted using #WxMaxima. The three #trajectories, shown in red, green and blue are for three fairly nearby #InitialConditions.

#DynamicalSystems #ChaoticAttractors #StrangeAttractors #NumericalSolutions #Mathematics #AppliedMathematics #CCBYSA #FreeSoftware

My commentary on our 2023 LIDA paper just got published! In it, I explore the idea that the behavioral and cognitive dispositions our original paper was concerned with may be understood as topological features of cognitive subsystems:

https://journals.sagepub.com/doi/10.1177/00368504241245812

#CogSci #Dispositions #DynamicalSystems #LIDA

I just updated the code and added one of the two fixed points and the according eigenvectors to the #RösslerAttractor plot, following the #PhasePlaneAnalysis discussion in this blog post: https://www.fabriziomusacchio.com/blog/2024-03-19-roesler_attractor_nullcines_and_fixed_points/

#PhasePortraits #DynamicalSystems

After some tuning time my new creation of a #nonlinear #DynamicalSystems example is ready for the showcase.

I call it dynamically accelerated PT2. The step response starts smooth as a PT2 but reaches the final value much faster (but still smoothly).

#control #engineers and #systemstheory

I will publish the formula soon but meanwhile I encourage you to guess how it is done.

Hints: #ODE system of order 4, analytic vectorfield ( i.e., rhs is ""even smoother" then C∞)

Genuary Prompt 13: Wobbly Function Day #genuary #genuary2024 #genuary13 #dynamicalsystems

I remember one time I ...found a book w/ pdf.
It was about displaying dynamical systems theory, showing manifolds and so on.
Plots were not made with any programming language, they were actual drawings, pastels, watercolors.
It's the type of book I literally have dreams about, but I think this one exists what was it?

Kindly boost my chances to find it

#maths #dynamicalsystems #topology #mathart #mathsart #scicomm

I spent a day last week with Python drawing phase portraits of the Bogdanov–Takens bifurcation for today's lecture. I hope it helps everybody understand what is happening.

I thought about writing a program with a nice GUI to help me draw phase portraits like this in order to "save" some time but that would take at least a week and fortunately I did not have time for that.

#DynamicalSystems

This week in our #DynamicalSystems course at #UPC we studied the effect of a hyperbolic saddle point in orbits of discrete maps. The periodically forced pendulum is a good example to simulate with #julialang ensemble simulations https://web.mat.upc.edu/joaquim.puig/J4DS/EnsembleParallel/EnsembleParallelPendulum.html