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arXiv · 2503.01498

Carleman-Fourier linearization of nonlinear real dynamical systems with quasi-periodic fields

Nader Motee·Qiyu Sun
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Abstract

This paper presents Carleman-Fourier linearization for analyzing nonlinear real dynamical systems with periodic vector fields. Using Fourier basis functions, this novel framework transforms such dynamical systems into equivalent infinite-dimensional linear dynamical systems. In this paper, we establish the exponential convergence of the primary block in the finite-section approximation of this linearized system to the state vector of the original nonlinear system. To showcase the efficacy of our approach, we apply it to the Kuramoto model, a prominent model for coupled oscillators. The results demonstrate promising accuracy in approximating the original system's behavior.

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Nader Motee, Qiyu Sun. 2025-03-03. Carleman-Fourier linearization of nonlinear real dynamical systems with quasi-periodic fields. https://arxiv.org/abs/2503.01498

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