A self-consistent framework with generalized local order parameters is derived for the Kuramoto model with dyadic and triadic interactions on hypergraphs, showing bistability onset depends on eigenvector correlations between dyadic and triadic structures.
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Exact dimensional reduction of N identical quasi-linear ODE units of order M to M+1 closed macroscopic equations that capture all microscopic dynamics.
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Mellin spectral theory on the multiplicative half-line reveals decoupling of geometric exponent a from spectral exponent b, with a=b marking simple RG fixed points and a≠b indicating multicriticality.
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Exact Dimensional Reduction for Quasi-Linear ODE Ensembles
Exact dimensional reduction of N identical quasi-linear ODE units of order M to M+1 closed macroscopic equations that capture all microscopic dynamics.