Transformability of Higher-order Network Dynamics

Transformability of Higher-order Network Dynamics | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Article Transformability of Higher-order Network Dynamics Shibo He, Ming Xie, Aming Li, Zi-Ke Zhang, Qihao Huang, Youxian Sun, and 1 more This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7125491/v1 This work is licensed under a CC BY 4.0 License Status: Published Journal Publication published 13 Mar, 2026 Read the published version in Communications Physics → Version 1 posted You are reading this latest preprint version Abstract Recent studies on higher-order network dynamics have primarily concentrated on intrinsic properties such as bistability and discontinuous phase transitions, while largely overlooking transformability— the ability of dynamics adaptation across different network structures, which fundamentally captures the essence of the dynamical processes. Here, we present a holistic analysis framework that elucidates the interplays between dynamics in pairwise and higher-order networks, demonstrating that these processes are not independent but can undergo systematic transformations. By focusing on contagion dynamics, we identify and quantify dynamical and structural factors that drive the transformability of higher-order network dynamics, uncovering a universal model for system instability governed by these factors. Furthermore, we validate the findings from contagion dynamics to opinion dynamics, showcasing its broad applicability across diverse dynamical processes. Our findings uncover the fundamental nature of dynamic transformability for shaping collective behaviors in higher-order networks, offering profound implications for modeling, predicting, and controlling dynamics in a wide range of real-world networked intelligent systems. Physical sciences/Physics/Statistical physics, thermodynamics and nonlinear dynamics/Complex networks Physical sciences/Mathematics and computing/Computational science Network dynamics Higher-order networks Network representations Full Text Additional Declarations There is NO Competing Interest. Supplementary Files SupplementaryInformationforTransformabilityofHigherorderNetworkDynamics.pdf Supplementary Information Cite Share Download PDF Status: Published Journal Publication published 13 Mar, 2026 Read the published version in Communications Physics → Version 1 posted You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. 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Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-7125491","acceptedTermsAndConditions":true,"allowDirectSubmit":false,"archivedVersions":[],"articleType":"Article","associatedPublications":[],"authors":[{"id":487072460,"identity":"8694d0d8-a4f6-4ff1-8f1a-3f4731082833","order_by":0,"name":"Shibo 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