Transformability of Higher-order Network Dynamics

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.