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arXiv · 2311.17186

Higher order interactions lead to "reluctant" synchrony breaking

Sören von der Gracht·Eddie Nijholt·Bob Rink
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Abstract

To model dynamical systems on networks with higher order (non-pairwise) interactions, we recently introduced a new class of ODEs on hypernetworks. Here we consider one-parameter synchrony breaking bifurcations in such ODEs. We call a synchrony breaking steady state branch ``reluctant'' if it is tangent to a synchrony space, but does not lie inside it. We prove that reluctant synchrony breaking is ubiquitous in hypernetwork systems, by constructing a large class of examples that support it. We also give an explicit formula for the order of tangency to the synchrony space of a reluctant steady state branch.

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Sören von der Gracht, Eddie Nijholt, Bob Rink. 2024-07-18. Higher order interactions lead to "reluctant" synchrony breaking. https://doi.org/10.1098/rspa.2023.0945

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