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PreprintCC BY 4.0arXiv

Low-Dimensional Phase Diagram of Higher-Order Networked Systems

  • Jia-Jie Qin
  • Jack Murdoch Moore
  • Xiaozhu Zhang
  • Gang Yan
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Abstract

Higher-order networks exhibit rich critical phenomena that cannot be captured by traditional pairwise models. Here, we develop an analytical dimension-reduction framework that maps higher-order networked dynamics onto an effective low-dimensional system, allowing accurate prediction of tipping boundaries, bistability regions, and the nature of phase transitions. We demonstrate the power of this framework across a range of dynamical processes, revealing distinct effects of higher-order interactions on transition continuity and hysteresis. Furthermore, we find that system resilience exhibits a profound dependence on the alignment between pairwise and higher-order connectivity, with assortative mixing enhancing tipping toward active states. Our findings establish a general theory for understanding the critical transitions in higher-order networks, offering new insights for anticipating and managing systemic risk in complex systems.

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Cite

BibTeXRIS
BibTeX
@misc{qin2026lowdimensional,
  title = {{Low-Dimensional Phase Diagram of Higher-Order Networked Systems}},
  author = {Jia-Jie Qin and Jack Murdoch Moore and Xiaozhu Zhang and Gang Yan},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.04692},
  eprint = {2609.04692},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.04692},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Low-Dimensional Phase Diagram of Higher-Order Networked Systems
AU  - Jia-Jie Qin
AU  - Jack Murdoch Moore
AU  - Xiaozhu Zhang
AU  - Gang Yan
PY  - 2026
DA  - 2026/09/04
PB  - arXiv
DO  - 10.48550/arxiv.2609.04692
UR  - https://arxiv.org/abs/2609.04692
AB  - Higher-order networks exhibit rich critical phenomena that cannot be captured by traditional pairwise models. Here, we develop an analytical dimension-reduction framework that maps higher-order networked dynamics onto an effective low-dimensional system, allowing accurate prediction of tipping boundaries, bistability regions, and the nature of phase transitions. We demonstrate the power of this framework across a range of dynamical processes, revealing distinct effects of higher-order interactions on transition continuity and hysteresis. Furthermore, we find that system resilience exhibits a profound dependence on the alignment between pairwise and higher-order connectivity, with assortative mixing enhancing tipping toward active states. Our findings establish a general theory for understanding the critical transitions in higher-order networks, offering new insights for anticipating and managing systemic risk in complex systems.
ER  -