Higher-order interactions lead to ‘reluctant’ synchrony breaking

S. von der Gracht, E. Nijholt, B. Rink, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 480 (2024).

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Journal Article | Published | English
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von der Gracht, SörenLibreCat ; Nijholt, Eddie; Rink, Bob
Abstract
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.
Publishing Year
Journal Title
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
Volume
480
Issue
2301
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von der Gracht S, Nijholt E, Rink B. Higher-order interactions lead to ‘reluctant’ synchrony breaking. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences. 2024;480(2301). doi:10.1098/rspa.2023.0945
von der Gracht, S., Nijholt, E., & Rink, B. (2024). Higher-order interactions lead to ‘reluctant’ synchrony breaking. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 480(2301). https://doi.org/10.1098/rspa.2023.0945
@article{von der Gracht_Nijholt_Rink_2024, title={Higher-order interactions lead to ‘reluctant’ synchrony breaking}, volume={480}, DOI={10.1098/rspa.2023.0945}, 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} }
Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Higher-Order Interactions Lead to ‘Reluctant’ Synchrony Breaking.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 480, no. 2301 (2024). https://doi.org/10.1098/rspa.2023.0945.
S. von der Gracht, E. Nijholt, and B. Rink, “Higher-order interactions lead to ‘reluctant’ synchrony breaking,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 480, no. 2301, 2024, doi: 10.1098/rspa.2023.0945.
von der Gracht, Sören, et al. “Higher-Order Interactions Lead to ‘Reluctant’ Synchrony Breaking.” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, vol. 480, no. 2301, The Royal Society, 2024, doi:10.1098/rspa.2023.0945.
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