
We are excited to host Eddie Nijholt (USP-São Carlos) in the BeyondTheEdge Seminar series:
Synchrony and synchrony-breaking as higher-order effects in hypernetwork systems
We start by introducing a novel framework for describing coupled cell systems with higher-order interactions as ODEs. This setup allows us to study how a hypernetwork structure influences the dynamics, and to what degree this differs from the classical network setting. For instance, just as for networks we find a natural notion of invariant synchrony space, and we generalise this to hypergraph fibrations. In the classical network setting, it is known that the linear systems determine all robust synchronisation patterns, but this is surprisingly not true for hypernetworks. Instead, it is necessary to consider nonlinear terms up to some fixed degree, which depends on the order of the hypernetwork. We give a formula for this degree, as well as a class of examples for which it is optimal. An interesting consequence is that some polydiagonal spaces may fail to be invariant solely because of the high-order terms in the hypernetwork system. This gives rise to intriguing generic bifurcation scenarios, where synchrony between nodes is broken at an unusually slow rate with respect to the bifurcation parameter. We prove rigorous results for these so-called "reluctant synchrony breaking" bifurcations. This is joint work with Sören von der Gracht and Bob Rink.
About the speaker
Eddie Nijholt completed his PhD at the Vrije Universiteit Amsterdam in 2018 under the supervision of Bob Rink and Jan Bouwe van den Berg. He then spent several years at the University of Urbana-Champaign in Illinois (US) funded by the Dutch Rubicon grant. After this he served as a co-principal investigator at USP, São Carlos (Brazil) and then as a Chapman fellow at Imperial College London (UK). He is currently a principal investigator at USP, funded by a FAPESP Young Investigator grant. His research interests include network dynamical systems, bifurcation theory, and complex systems, with a principal focus on developing rigorous techniques that deal with interaction structure and that are informed by algebraic and combinatorial methods.
Meeting information
TBA