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Maxime Lucas

@maximelca.bsky.social

184 followers 221 following 22 posts

Physicist. Complex systems, networks, and data. 🍄🐋 @UNamur @UCLouvain @ProjectCETI

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Maxime Lucas @maximelca.bsky.social · 04/06/2026

6. These rules can be used as a design principle: by smoothly tuning the symmetry of a modified Stuart-Landau oscillator, we tune the resulting phase coupling functions.

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Maxime Lucas @maximelca.bsky.social · 04/06/2026

5. Numerics confirm these rules across diverse oscillators F and coupling functions G:

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Maxime Lucas @maximelca.bsky.social · 04/06/2026

4. Simple rules determine which phase coupling emerge (or not) only based on the symmetries of the original nonlinear dynamics F and coupling G. van der Pol (odd F) → single three-body coupling as soon as G is symmetric in Xj (focus oscillator). But the Brusselator (F not odd) → mix of couplings.

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Maxime Lucas @maximelca.bsky.social · 04/06/2026

3. For pairwise interactions, the Kuramoto coupling can be obtained from nonlinear oscillators by phase reduction. Phase reduction can also tell us for higher-order ones, but it's analytically challenging and only a handful of cases are known. What if we didn't need to perform phase reduction?

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Maxime Lucas @maximelca.bsky.social · 04/06/2026

2. For pairwise interactions, there's a single coupling, Kuramoto's: sin(−θj+θk). But for higher-order ones, there's many more, e.g. sin(−2θj+θk+θl) and sin(−θj+2θk− θl) for 3- bodies, and their dynamics differ! So, which couplings should we choose? And what physical models do they represent?

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Maxime Lucas @maximelca.bsky.social · 04/06/2026

Which coupling functions should you use in your higher-order Kuramoto model? Symmetries will tell you! "Symmetry-based selection rules for higher-order interactions in coupled oscillators" preprint now out. Preprint: arxiv.org/abs/2606.04904 Code: tiny.cc/60l4101 w/ I. Léon, R. Muolo, Y. Zhang 🧵1/

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Maxime Lucas @maximelca.bsky.social · 12/02/2026

We use a cost function based on information theory and diffusion processes. In brief, some empirical systems require higher-order structure, but pairwise models are sufficient for some others. 2/

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Maxime Lucas @maximelca.bsky.social · 12/02/2026

When should we favour a model with higher-order interactions over classical pairwise ones? "Reducibility of higher-order networks from dynamics" is now out in @natcomms.nature.com Paper: rdcu.be/e3tH4 Code: t.ly/pdELP w/ @lgajo.bsky.social A. Ghavasieh @fede7j.bsky.social @manlius.bsky.social 🧵1/

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Maxime Lucas @maximelca.bsky.social · 05/06/2025

@nwlandry.bsky.social fighting against vibes-based estimations of the convergence when sampling from the configuration model. Good content. Bonus: @xgi.bsky.social viz

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Maxime Lucas @maximelca.bsky.social · 03/06/2025

Our first keynote @marilyngatica.bsky.social opening TopoNets @netsciconf.bsky.social with higher-order interactions for neuroscience

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