{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,1]],"date-time":"2026-04-01T22:26:45Z","timestamp":1775082405260,"version":"3.50.1"},"reference-count":40,"publisher":"Oxford University Press (OUP)","issue":"2","license":[{"start":{"date-parts":[[2024,3,5]],"date-time":"2024-03-05T00:00:00Z","timestamp":1709596800000},"content-version":"vor","delay-in-days":13,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"published-print":{"date-parts":[[2024,2,21]]},"abstract":"<jats:title>Abstract<\/jats:title>\n               <jats:p>Heteroclinic structures organize global features of dynamical systems. We analyse whether heteroclinic structures can arise in network dynamics with higher-order interactions which describe the nonlinear interactions between three or more units. We find that while commonly analysed model equations such as network dynamics on undirected hypergraphs may be useful to describe local dynamics such as cluster synchronization, they give rise to obstructions that allow to design of heteroclinic structures in phase space. By contrast, directed hypergraphs break the homogeneity and lead to vector fields that support heteroclinic structures.<\/jats:p>","DOI":"10.1093\/comnet\/cnae009","type":"journal-article","created":{"date-parts":[[2024,3,5]],"date-time":"2024-03-05T13:21:10Z","timestamp":1709644870000},"source":"Crossref","is-referenced-by-count":4,"title":["Heteroclinic dynamics in network dynamical systems with higher-order interactions"],"prefix":"10.1093","volume":"12","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5238-1146","authenticated-orcid":false,"given":"Christian","family":"Bick","sequence":"first","affiliation":[{"name":"Department of Mathematics, Vrije Universiteit Amsterdam , De Boelelaan 1111 , 1081 HV Amsterdam, The Netherlands"},{"name":"Department of Mathematics, University of Exeter , Exeter EX4 4QF, United Kingdom"},{"name":"Mathematical Institute, University of Oxford , Oxford OX2 6GG, United Kingdom"},{"name":"Institute for Advanced Study, Technical University of Munich , Lichtenbergstr 2 , 85748 Garching, Germany"}]},{"given":"S\u00f6ren","family":"von der Gracht","sequence":"additional","affiliation":[{"name":"Institute of Mathematics, Paderborn University , Warburger Str. 100 , 33098 Paderborn, Germany"}]}],"member":"286","published-online":{"date-parts":[[2024,3,4]]},"reference":[{"key":"2024030513210764400_cnae009-B1","volume-title":"Synchronization: A Universal Concept in Nonlinear Sciences","author":"Pikovsky","year":"2003"},{"key":"2024030513210764400_cnae009-B2","volume-title":"Sync: The Emerging Science of Spontaneous Order","author":"Strogatz","year":"2004"},{"key":"2024030513210764400_cnae009-B3","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2020.05.004","article-title":"Networks beyond pairwise interactions: structure and dynamics","volume":"874","author":"Battiston","year":"2020","journal-title":"Phys. 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