[{"language":[{"iso":"eng"}],"doi":"10.1137/23m1561075","year":"2023","title":"Hypernetworks: Cluster Synchronization Is a Higher-Order Effect","author":[{"orcid":"0000-0002-8054-2058","first_name":"Sören","last_name":"von der Gracht","full_name":"von der Gracht, Sören","id":"97359"},{"full_name":"Nijholt, Eddie","last_name":"Nijholt","first_name":"Eddie"},{"full_name":"Rink, Bob","last_name":"Rink","first_name":"Bob"}],"publication_identifier":{"issn":["0036-1399","1095-712X"]},"date_updated":"2023-11-29T10:52:23Z","publication_status":"published","intvolume":"        83","date_created":"2023-11-29T10:50:05Z","keyword":["Applied Mathematics"],"type":"journal_article","department":[{"_id":"101"}],"issue":"6","publication":"SIAM Journal on Applied Mathematics","abstract":[{"lang":"eng","text":"Many networked systems are governed by non-pairwise interactions between nodes. The resulting higher-order interaction structure can then be encoded by means of a hypernetwork. In this paper we consider dynamical systems on hypernetworks by defining a class of admissible maps for every such hypernetwork. We explain how to classify robust cluster synchronization patterns on hypernetworks by finding balanced partitions, and we generalize the concept of a graph fibration to the hypernetwork context. We also show that robust synchronization patterns are only fully determined by polynomial admissible maps of high order. This means that, unlike in dyadic networks, cluster synchronization on hypernetworks is a higher-order, i.e., nonlinear, effect. We give a formula, in terms of the order of the hypernetwork, for the degree of the polynomial admissible maps that determine robust synchronization patterns. We also demonstrate that this degree is optimal by investigating a class of examples. We conclude by demonstrating how this effect may cause remarkable synchrony breaking bifurcations that occur at high polynomial degree."}],"page":"2329-2353","_id":"49326","publisher":"Society for Industrial & Applied Mathematics (SIAM)","user_id":"97359","volume":83,"status":"public","external_id":{"arxiv":["2302.08974"]},"citation":{"short":"S. von der Gracht, E. Nijholt, B. Rink, SIAM Journal on Applied Mathematics 83 (2023) 2329–2353.","chicago":"Gracht, Sören von der, Eddie Nijholt, and Bob Rink. “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect.” <i>SIAM Journal on Applied Mathematics</i> 83, no. 6 (2023): 2329–53. <a href=\"https://doi.org/10.1137/23m1561075\">https://doi.org/10.1137/23m1561075</a>.","apa":"von der Gracht, S., Nijholt, E., &#38; Rink, B. (2023). Hypernetworks: Cluster Synchronization Is a Higher-Order Effect. <i>SIAM Journal on Applied Mathematics</i>, <i>83</i>(6), 2329–2353. <a href=\"https://doi.org/10.1137/23m1561075\">https://doi.org/10.1137/23m1561075</a>","ieee":"S. von der Gracht, E. Nijholt, and B. Rink, “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect,” <i>SIAM Journal on Applied Mathematics</i>, vol. 83, no. 6, pp. 2329–2353, 2023, doi: <a href=\"https://doi.org/10.1137/23m1561075\">10.1137/23m1561075</a>.","ama":"von der Gracht S, Nijholt E, Rink B. Hypernetworks: Cluster Synchronization Is a Higher-Order Effect. <i>SIAM Journal on Applied Mathematics</i>. 2023;83(6):2329-2353. doi:<a href=\"https://doi.org/10.1137/23m1561075\">10.1137/23m1561075</a>","bibtex":"@article{von der Gracht_Nijholt_Rink_2023, title={Hypernetworks: Cluster Synchronization Is a Higher-Order Effect}, volume={83}, DOI={<a href=\"https://doi.org/10.1137/23m1561075\">10.1137/23m1561075</a>}, number={6}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}, year={2023}, pages={2329–2353} }","mla":"von der Gracht, Sören, et al. “Hypernetworks: Cluster Synchronization Is a Higher-Order Effect.” <i>SIAM Journal on Applied Mathematics</i>, vol. 83, no. 6, Society for Industrial &#38; Applied Mathematics (SIAM), 2023, pp. 2329–53, doi:<a href=\"https://doi.org/10.1137/23m1561075\">10.1137/23m1561075</a>."}},{"publication":"SIAM Journal on Applied Mathematics","issue":"5","type":"journal_article","keyword":["Applied Mathematics"],"date_created":"2024-04-07T12:52:03Z","intvolume":"        83","date_updated":"2024-04-07T12:52:06Z","publication_status":"published","author":[{"full_name":"Painter, Kevin J.","last_name":"Painter","first_name":"Kevin J."},{"full_name":"Winkler, Michael","last_name":"Winkler","first_name":"Michael"}],"publication_identifier":{"issn":["0036-1399","1095-712X"]},"year":"2023","title":"Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities","doi":"10.1137/22m1539393","language":[{"iso":"eng"}],"citation":{"ieee":"K. J. Painter and M. Winkler, “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities,” <i>SIAM Journal on Applied Mathematics</i>, vol. 83, no. 5, pp. 2096–2117, 2023, doi: <a href=\"https://doi.org/10.1137/22m1539393\">10.1137/22m1539393</a>.","apa":"Painter, K. J., &#38; Winkler, M. (2023). Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities. <i>SIAM Journal on Applied Mathematics</i>, <i>83</i>(5), 2096–2117. <a href=\"https://doi.org/10.1137/22m1539393\">https://doi.org/10.1137/22m1539393</a>","short":"K.J. Painter, M. Winkler, SIAM Journal on Applied Mathematics 83 (2023) 2096–2117.","chicago":"Painter, Kevin J., and Michael Winkler. “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities.” <i>SIAM Journal on Applied Mathematics</i> 83, no. 5 (2023): 2096–2117. <a href=\"https://doi.org/10.1137/22m1539393\">https://doi.org/10.1137/22m1539393</a>.","mla":"Painter, Kevin J., and Michael Winkler. “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities.” <i>SIAM Journal on Applied Mathematics</i>, vol. 83, no. 5, Society for Industrial &#38; Applied Mathematics (SIAM), 2023, pp. 2096–117, doi:<a href=\"https://doi.org/10.1137/22m1539393\">10.1137/22m1539393</a>.","bibtex":"@article{Painter_Winkler_2023, title={Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities}, volume={83}, DOI={<a href=\"https://doi.org/10.1137/22m1539393\">10.1137/22m1539393</a>}, number={5}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Painter, Kevin J. and Winkler, Michael}, year={2023}, pages={2096–2117} }","ama":"Painter KJ, Winkler M. Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities. <i>SIAM Journal on Applied Mathematics</i>. 2023;83(5):2096-2117. doi:<a href=\"https://doi.org/10.1137/22m1539393\">10.1137/22m1539393</a>"},"status":"public","volume":83,"user_id":"31496","_id":"53340","publisher":"Society for Industrial & Applied Mathematics (SIAM)","page":"2096-2117"},{"publication":"SIAM Journal on Applied Mathematics","issue":"5","citation":{"short":"K.J. Painter, M. Winkler, SIAM Journal on Applied Mathematics 83 (2023) 2096–2117.","chicago":"Painter, Kevin J., and Michael Winkler. “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities.” <i>SIAM Journal on Applied Mathematics</i> 83, no. 5 (2023): 2096–2117. <a href=\"https://doi.org/10.1137/22m1539393\">https://doi.org/10.1137/22m1539393</a>.","ieee":"K. J. Painter and M. Winkler, “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities,” <i>SIAM Journal on Applied Mathematics</i>, vol. 83, no. 5, pp. 2096–2117, 2023, doi: <a href=\"https://doi.org/10.1137/22m1539393\">10.1137/22m1539393</a>.","apa":"Painter, K. J., &#38; Winkler, M. (2023). Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities. <i>SIAM Journal on Applied Mathematics</i>, <i>83</i>(5), 2096–2117. <a href=\"https://doi.org/10.1137/22m1539393\">https://doi.org/10.1137/22m1539393</a>","bibtex":"@article{Painter_Winkler_2023, title={Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities}, volume={83}, DOI={<a href=\"https://doi.org/10.1137/22m1539393\">10.1137/22m1539393</a>}, number={5}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Painter, Kevin J. and Winkler, Michael}, year={2023}, pages={2096–2117} }","ama":"Painter KJ, Winkler M. Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities. <i>SIAM Journal on Applied Mathematics</i>. 2023;83(5):2096-2117. doi:<a href=\"https://doi.org/10.1137/22m1539393\">10.1137/22m1539393</a>","mla":"Painter, Kevin J., and Michael Winkler. “Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities.” <i>SIAM Journal on Applied Mathematics</i>, vol. 83, no. 5, Society for Industrial &#38; Applied Mathematics (SIAM), 2023, pp. 2096–117, doi:<a href=\"https://doi.org/10.1137/22m1539393\">10.1137/22m1539393</a>."},"date_created":"2025-12-18T19:15:29Z","type":"journal_article","year":"2023","status":"public","title":"Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities","author":[{"last_name":"Painter","first_name":"Kevin J.","full_name":"Painter, Kevin J."},{"id":"31496","full_name":"Winkler, Michael","first_name":"Michael","last_name":"Winkler"}],"publication_identifier":{"issn":["0036-1399","1095-712X"]},"date_updated":"2025-12-18T20:11:36Z","publication_status":"published","intvolume":"        83","page":"2096-2117","_id":"63277","publisher":"Society for Industrial & Applied Mathematics (SIAM)","language":[{"iso":"eng"}],"doi":"10.1137/22m1539393","user_id":"31496","volume":83},{"doi":"10.1137/19m1250261","user_id":"31496","volume":79,"page":"1990-2010","publisher":"Society for Industrial & Applied Mathematics (SIAM)","_id":"63349","language":[{"iso":"eng"}],"date_updated":"2025-12-19T10:47:44Z","publication_status":"published","intvolume":"        79","year":"2019","status":"public","title":"Occurrence vs. Absence of Taxis-Driven Instabilities in a May--Nowak Model for Virus Infection","publication_identifier":{"issn":["0036-1399","1095-712X"]},"author":[{"full_name":"Bellomo, Nicola","first_name":"Nicola","last_name":"Bellomo"},{"first_name":"Kevin J.","last_name":"Painter","full_name":"Painter, Kevin J."},{"full_name":"Tao, Youshan","last_name":"Tao","first_name":"Youshan"},{"first_name":"Michael","last_name":"Winkler","full_name":"Winkler, Michael","id":"31496"}],"type":"journal_article","date_created":"2025-12-19T10:47:32Z","publication":"SIAM Journal on Applied Mathematics","issue":"5","citation":{"ama":"Bellomo N, Painter KJ, Tao Y, Winkler M. Occurrence vs. Absence of Taxis-Driven Instabilities in a May--Nowak Model for Virus Infection. <i>SIAM Journal on Applied Mathematics</i>. 2019;79(5):1990-2010. doi:<a href=\"https://doi.org/10.1137/19m1250261\">10.1137/19m1250261</a>","bibtex":"@article{Bellomo_Painter_Tao_Winkler_2019, title={Occurrence vs. Absence of Taxis-Driven Instabilities in a May--Nowak Model for Virus Infection}, volume={79}, DOI={<a href=\"https://doi.org/10.1137/19m1250261\">10.1137/19m1250261</a>}, number={5}, journal={SIAM Journal on Applied Mathematics}, publisher={Society for Industrial &#38; Applied Mathematics (SIAM)}, author={Bellomo, Nicola and Painter, Kevin J. and Tao, Youshan and Winkler, Michael}, year={2019}, pages={1990–2010} }","mla":"Bellomo, Nicola, et al. “Occurrence vs. Absence of Taxis-Driven Instabilities in a May--Nowak Model for Virus Infection.” <i>SIAM Journal on Applied Mathematics</i>, vol. 79, no. 5, Society for Industrial &#38; Applied Mathematics (SIAM), 2019, pp. 1990–2010, doi:<a href=\"https://doi.org/10.1137/19m1250261\">10.1137/19m1250261</a>.","short":"N. Bellomo, K.J. Painter, Y. Tao, M. Winkler, SIAM Journal on Applied Mathematics 79 (2019) 1990–2010.","chicago":"Bellomo, Nicola, Kevin J. Painter, Youshan Tao, and Michael Winkler. “Occurrence vs. Absence of Taxis-Driven Instabilities in a May--Nowak Model for Virus Infection.” <i>SIAM Journal on Applied Mathematics</i> 79, no. 5 (2019): 1990–2010. <a href=\"https://doi.org/10.1137/19m1250261\">https://doi.org/10.1137/19m1250261</a>.","apa":"Bellomo, N., Painter, K. J., Tao, Y., &#38; Winkler, M. (2019). Occurrence vs. Absence of Taxis-Driven Instabilities in a May--Nowak Model for Virus Infection. <i>SIAM Journal on Applied Mathematics</i>, <i>79</i>(5), 1990–2010. <a href=\"https://doi.org/10.1137/19m1250261\">https://doi.org/10.1137/19m1250261</a>","ieee":"N. Bellomo, K. J. Painter, Y. Tao, and M. Winkler, “Occurrence vs. Absence of Taxis-Driven Instabilities in a May--Nowak Model for Virus Infection,” <i>SIAM Journal on Applied Mathematics</i>, vol. 79, no. 5, pp. 1990–2010, 2019, doi: <a href=\"https://doi.org/10.1137/19m1250261\">10.1137/19m1250261</a>."}}]