An explicit algebraic solution for the global phase trajectories of the N=3 identical all-to-all Kuramoto model is constructed via Koopman eigenfunctions that reduce the dynamics to solvable time-dependent quartic equations.
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kEDMD for stochastic systems has L^∞ error bounds that separate a deterministic fill-distance term from a probabilistic Monte Carlo sampling term.
The orthogonal dynamics for Mori's projection is a strongly continuous semigroup generated by QL Q, with the GLE and 2FDT holding for autonomous systems whose evolution is a strongly continuous semigroup
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Global Analytical Solution of the Identical Kuramoto Model for N=3 via Koopman Eigenfunctions
An explicit algebraic solution for the global phase trajectories of the N=3 identical all-to-all Kuramoto model is constructed via Koopman eigenfunctions that reduce the dynamics to solvable time-dependent quartic equations.
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Koopman for stochastic dynamics: error bounds for kernel extended dynamic mode decomposition
kEDMD for stochastic systems has L^∞ error bounds that separate a deterministic fill-distance term from a probabilistic Monte Carlo sampling term.
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On the generalized Langevin equation and the Mori projection operator technique
The orthogonal dynamics for Mori's projection is a strongly continuous semigroup generated by QL Q, with the GLE and 2FDT holding for autonomous systems whose evolution is a strongly continuous semigroup