@article{49326,
  abstract     = {{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.}},
  author       = {{von der Gracht, Sören and Nijholt, Eddie and Rink, Bob}},
  issn         = {{0036-1399}},
  journal      = {{SIAM Journal on Applied Mathematics}},
  keywords     = {{Applied Mathematics}},
  number       = {{6}},
  pages        = {{2329--2353}},
  publisher    = {{Society for Industrial & Applied Mathematics (SIAM)}},
  title        = {{{Hypernetworks: Cluster Synchronization Is a Higher-Order Effect}}},
  doi          = {{10.1137/23m1561075}},
  volume       = {{83}},
  year         = {{2023}},
}

@article{53340,
  author       = {{Painter, Kevin J. and Winkler, Michael}},
  issn         = {{0036-1399}},
  journal      = {{SIAM Journal on Applied Mathematics}},
  keywords     = {{Applied Mathematics}},
  number       = {{5}},
  pages        = {{2096--2117}},
  publisher    = {{Society for Industrial & Applied Mathematics (SIAM)}},
  title        = {{{Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities}}},
  doi          = {{10.1137/22m1539393}},
  volume       = {{83}},
  year         = {{2023}},
}

@article{63277,
  author       = {{Painter, Kevin J. and Winkler, Michael}},
  issn         = {{0036-1399}},
  journal      = {{SIAM Journal on Applied Mathematics}},
  number       = {{5}},
  pages        = {{2096--2117}},
  publisher    = {{Society for Industrial & Applied Mathematics (SIAM)}},
  title        = {{{Phenotype Switching in Chemotaxis Aggregation Models Controls the Spontaneous Emergence of Large Densities}}},
  doi          = {{10.1137/22m1539393}},
  volume       = {{83}},
  year         = {{2023}},
}

@article{63349,
  author       = {{Bellomo, Nicola and Painter, Kevin J. and Tao, Youshan and Winkler, Michael}},
  issn         = {{0036-1399}},
  journal      = {{SIAM Journal on Applied Mathematics}},
  number       = {{5}},
  pages        = {{1990--2010}},
  publisher    = {{Society for Industrial & Applied Mathematics (SIAM)}},
  title        = {{{Occurrence vs. Absence of Taxis-Driven Instabilities in a May--Nowak Model for Virus Infection}}},
  doi          = {{10.1137/19m1250261}},
  volume       = {{79}},
  year         = {{2019}},
}