Fantastic, well deserved.

Simply: The dynamics themselves do not go away, but making things more generic helps understand how they organize the dynamics more generally.

Not the interactions themselves. Sometimes they are just too special and give rise to extra symmetries.

Dynamics on invariant tori emerging through forced symmetry breaking in phase oscillator networks We consider synchrony patterns in coupled phase oscillator networks that correspond to invariant tori. For specific nongeneric coupling, these tori are equilibria relative to a continuous symmetry act...

Let's break some structures imposed by higher-order interactions! We compute how things deform and what remains when continuous symmetries are broken. For now freely available at www.aimsciences.org/article/doi/... (but also at arXiv:2408.02119).

A summary of the results are now also part of a @oxfordmathematics.bsky.social Research Case Study: www.maths.ox.ac.uk/node/74552

Higher-order phase reduction for delay-coupled oscillators beyond the phase-shift approximation Network interactions between dynamical units are often subject to time delay. We develop a phase reduction method for delay-coupled oscillator networks. The method is based on rewriting the delay-diff...

"Higher-order phase reduction for delay-coupled oscillators beyond the phase-shift approximation" now on the arXiv at arxiv.org/abs/2510.27524.

Reducing the dimensions of adaptive networks Framework for decreasing the dimensionality of complex systems facilitates analysis of complexity.

The nice summary "Reducing the dimensions of adaptive networks" for a broader audience was published alongside the paper at doi.org/10.1063/10.0...

This motivates new mathematical insights into the multiple time scale dynamics of adaptive networks. And opens up questions how constraints and adaptive dependency is realized in real world adaptive networks.

We introduce constraints to the adaptive dynamics as a way to reduce dimensionality. These may be intrinsic, for example, if the adaptation rule is nondirectional. Or they may be forced by a homeostasis mechanism.

Adaptivity is a crucial ingredient of many networked systems, but a key issue is their high-dimensionality. A dense network of N nodes has O(N^2) adaptive connections.

Multiple timescale dynamics of network adaptation with constraints Adaptive network dynamical systems describe the co-evolution of dynamical quantities on the nodes and the dynamics of the network connections themselves. For de

New paper with @math-martens.bsky.social on "Multiple timescale dynamics of network adaptation with constraints" now available Open Access in Chaos: doi.org/10.1063/5.02...

Global South Fellowship Scheme The Global South Plan of the Faculty of Science (FNWI) at the University of Amsterdam (UvA) offers four fellowships to talented scientists from the Global South to visit our Faculty for a few months a...

🥼Global South Fellowship!
DIEP is co-hosting one fellowship for a researcher from the Global South to work on subjects related to the Research Priority Area: Emergent Phenomena in Society in Amsterdam!
🚨Deadline to apply: 15/11 midnight
Please share!
More info: www.uva.nl/en/about-the...

We just advertised the Hooke Fellowships for exceptional researchers (typically after their first post-doc).

You are completely free to set up your own research agenda for three years.

RT please

my.corehr.com/pls/uoxrecru...

Lots of higher-order interactions at the joint @beyondtheedge.network and RUNES workshop at AMU in Marseille this week. Thanks to @alainbarrat.bsky.social and @lordgrilo.bsky.social!

Happening soon with the fantastic @haharrington.bsky.social. Join us!

How many points converge to a heteroclinic network in an aperiodic way? Homoclinic and heteroclinic connections can form cycles and networks in phase space, which organize global phenomena in dynamical systems. On the one hand, stability notions for (omni)cycles give i...

Ever wondered how many points converge to a heteroclinic network in an aperiodic way? doi.org/10.1080/1468...

BeyondTheEdge goes to Sicily BeyondTheEdge researchers participated in the School of Complexity on

BeyondTheEdge at the School of Complexity on "Higher-order interactions: mechanisms, behaviors, and networks" by our own @lordgrilo.bsky.social and @gin-bianconi.bsky.social with @aliceschwarze.bsky.social, @danielemarinazzo.bsky.social. Great perspectives! www.beyondtheedge.network/articles/bey...

Decoding how higher-order network interactions shape contagion dynamics - Journal of Mathematical Biology Complex contagion models that involve contagion along higher-order structures, such as simplicial complexes and hypergraphs, yield new classes of mean-field models. Interestingly, the differential equ...

Fun collaborative project with Istvan Z. Kiss (London) and Peter Simon to understand how higher-order interactions affect the dynamics of contagion processes now out in J Math Bio: doi.org/10.1007/s002...

I am extremely excited that my Istvan Z. Kiss number now is one with multiplicity 2!

Going #BeyondTheEdge in Aachen! Great fun catching up with @beyondtheedge.network colleagues at the HOOC workshop organized by M Schaub: conf.netsci.rwth-aachen.de

"Free yourself with constraints" is a good summary of the work.

Multiple Timescale Dynamics of Network Adaptation with Constraints Adaptive network dynamical systems describe the co-evolution of dynamical quantities on the nodes as well as dynamics of the network connections themselves. For dense networks of many nodes, the resul...

Adaptive network dynamics are too high dimensional? Constrain! Or maybe adaptation may be naturally constrained to low-dimensional dynamics? Joint work with
@math-martens.bsky.social
now on the arXiv at arxiv.org/abs/2507.06359.

Maybe I should use generative AI to plot any vector field in the style of ancient nails...

Ancient vector fields excavated close to Dynamics Days Europe 2025 in Thessaloniki. It was a fun conference (just too short), see you in Lisbon next year!

Frequency synchronization induced by frequency detuning Analyses and experiments on multistable networks show that frequency detuning can promote synchronization.

If you couple two systems with bistability between oscillations of distinct effective frequencies, you have to make them different for the distinct states to synchronize in frequency. Some theory and experiments now in Science Advances. doi.org/10.1126/scia...

Indeed, great to see so many of you! And of course thanks to @andai.bsky.social and @piratepeel.bsky.social for making NetSci 2025 happen.

Can a network be physically be a graph but effectively be a hypergraph? Tiago Pereira is speaking about emergent hypernetworks in the focus session “Network Dynamical Systems” at @netsciconf.bsky.social.

Come to the Focus Session "Network Dynamical Systems" at @netsciconf.bsky.social Friday afternoon for a free copy of Bear Networks! www.beyondtheedge.network/resources/be... #NetSci2025

0 mod 10 workshop We are excited to announce a Workshop on Dynamical Systems at the Amsterdam Center of Dynamics and Computation of the Vrije Universiteit Amsterdam. The workshop, organised by Chris Bick and Bob Rink, ...

Join us July 9-11 at the Amsterdam Center for Dynamics and Computation to celebrate dynamical systems theory and application as well as two 0 mod 10 birthdays! Register now at www.amsterdam-dynamics.nl/zero-mod-ten/

You've got friends round for coffee and cake. There are seven of you. Trouble is, you've made a square cake. How do you make sure everyone receives an equal share?

Dominic has his cake and they all eat it.