Higher order interactions lead to "reluctant" synchrony breaking
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2023
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| _version_ | 1866929425551982592 |
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| author | von der Gracht, Sören Nijholt, Eddie Rink, Bob |
| author_facet | von der Gracht, Sören Nijholt, Eddie Rink, Bob |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_17186 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Higher order interactions lead to "reluctant" synchrony breaking von der Gracht, Sören Nijholt, Eddie Rink, Bob Dynamical Systems 37G10, 05C65 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. |
| title | Higher order interactions lead to "reluctant" synchrony breaking |
| topic | Dynamical Systems 37G10, 05C65 |
| url | https://arxiv.org/abs/2311.17186 |