ACDC Seminar by Fergal Murphy on the 14th of April

On 14-04-2026 at 16:00, Fergal Murphy (Technical University of Munich) will give an Amsterdam Dynamics Seminar. Note that this seminar will take place on a Tuesday instead of the regular Wednesday! We will go for drinks at Bar Boele after the talk.

The talk will take place in the Maryam seminar room (9A-46).

Title: Emergent Higher-Order Structure from Fast Adaptive Networks: Reduction and Continuum Limits

Abstract: Many higher-order network models postulate multi-body interactions from the outset. In this talk, we discuss a different mechanism: the emergence of effective higher-order structure from an underlying adaptive system that is microscopically pairwise.

We consider adaptive phase oscillator networks in which the coupling weights evolve on a fast timescale relative to the node dynamics. Using geometric singular perturbation theory, we eliminate the fast edge variables via slow-manifold reduction and show that the resulting reduced phase dynamics is generically no longer pairwise representable: already at first order, genuine triplet interaction terms appear.

We then study the large-network limit. Passing to a dense-graph continuum description, we compare reducing first and then taking the continuum limit with taking the continuum limit first and then reducing in an infinite-dimensional setting. We show that these two procedures commute to first order, so the emergent triplet structure persists in the continuum limit and is not a finite-size artefact.

This is joint work with Christian Kuehn and Jan-Eric Sulzbach.

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