article published Sören von der Gracht author 973590000-0002-8054-2058 Eddie Nijholt author Bob Rink author 101 department To model dynamical systems on networks with higher-order (non-pairwise) interactions, we recently introduced a new class of ordinary differential equations (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. https://ris.uni-paderborn.de/download/59171/59172/higher-order-interactions-lead-to-reluctant-synchrony-breaking.pdf application/pdfno The Royal Society2024 eng higher-order interactionssynchrony breakingnetwork dynamicscoupled cell systems 1364-5021 1471-294610.1098/rspa.2023.0945 4802301 von der Gracht S, Nijholt E, Rink B. Higher-order interactions lead to ‘reluctant’ synchrony breaking. <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>. 2024;480(2301). doi:<a href="https://doi.org/10.1098/rspa.2023.0945">10.1098/rspa.2023.0945</a> @article{von der Gracht_Nijholt_Rink_2024, title={Higher-order interactions lead to ‘reluctant’ synchrony breaking}, volume={480}, DOI={<a href="https://doi.org/10.1098/rspa.2023.0945">10.1098/rspa.2023.0945</a>}, number={2301}, journal={Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences}, publisher={The Royal Society}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2024} } von der Gracht, Sören, et al. “Higher-Order Interactions Lead to ‘Reluctant’ Synchrony Breaking.” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 480, no. 2301, The Royal Society, 2024, doi:<a href="https://doi.org/10.1098/rspa.2023.0945">10.1098/rspa.2023.0945</a>. Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Higher-Order Interactions Lead to ‘Reluctant’ Synchrony Breaking.” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i> 480, no. 2301 (2024). <a href="https://doi.org/10.1098/rspa.2023.0945">https://doi.org/10.1098/rspa.2023.0945</a>. S. von der Gracht, E. Nijholt, B. Rink, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 480 (2024). von der Gracht, S., Nijholt, E., &#38; Rink, B. (2024). Higher-order interactions lead to ‘reluctant’ synchrony breaking. <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, <i>480</i>(2301). <a href="https://doi.org/10.1098/rspa.2023.0945">https://doi.org/10.1098/rspa.2023.0945</a> S. von der Gracht, E. Nijholt, and B. Rink, “Higher-order interactions lead to ‘reluctant’ synchrony breaking,” <i>Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences</i>, vol. 480, no. 2301, 2024, doi: <a href="https://doi.org/10.1098/rspa.2023.0945">10.1098/rspa.2023.0945</a>. 591712025-03-27T10:15:06Z2025-03-27T10:19:56Z