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.
A one-dimensional reduction for dynamical systems on networks with purely higher-order interactions is developed, formulated through an effective higher-order interaction strength, associated with the triangular interactions of the underlying network and the dynamical system's effective state.
Amit Tiwari, C. Hens, Prosenjit Kundu· Proceedings of the Royal Soc...· 1 citation
We derive a one-dimensional reduction for nonlinear dynamics on simplicial complexes containing both pairwise and triangular (higher-order) interactions. The effective state is defined using a mixed weight determined by the pairwise and triangular degrees of each node. The resulting reduced equation retains two structu...
Amit Tiwari, C. Hens, Prosenjit Kundu· 0 citations
We study a high-dimensional Kuramoto model with attractive pairwise coupling and a repulsive higher-order effect. Although the pairwise interaction favors synchronization, the higher-order interaction prevents complete synchronization and selects an intermediate level of coherence corresponding to the balanced equilibr...
Can asymmetry between two interacting networks fundamentally change how they synchronize? We identify double explosive transitions in the forward direction, backward direction, or a combination thereof, with single or double hysteresis loops in an adaptive bilayer multiplex network of Kuramoto oscillators with pairwise...
Inferring network structure from dynamical observations is a fundamental inverse problem in complex systems. Existing approaches have largely focused on single-layer or pairwise interaction networks, leaving the reconstructability of multiplex systems with higher-order interactions poorly understood. Here, we show that...
Guang-Yuan Mei, Yao Cai, Suo-Yi Tan et al.· 0 citations
Explosive death —a discontinuous, first-order transition from oscillatory dynamics to a steady state— is investigated in a framework of interacting networks under mixed coupling. Unlike previous studies focused on monolayer topologies, this work explores the interplay between local diffusive coupling among peripheral n...
Ranjib Banerjee, Dibakar Ghosh, Amit Sharma· Europhysics letters· 0 citations
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