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math.DS2025
Beyond Carleman Linearization of Nonlinear Dynamical System: Insights from a Case Study
Panpan Chen, Nader Motee, Qiyu Sun
Nonlinear dynamical systems are widely encountered in various scientific and engineering fields. Despite significant advances in theoretical understanding, developing complete and…
math.DS2025
Carleman-Fourier linearization of nonlinear real dynamical systems with quasi-periodic fields
Nader Motee, Qiyu Sun
This paper presents Carleman-Fourier linearization for analyzing nonlinear real dynamical systems with periodic vector fields. Using Fourier basis functions, this novel framework t…
math.DS2024
Carleman-Fourier Linearization of Complex Dynamical Systems: Convergence and Explicit Error Bounds
Panpan Chen, Nader Motee, Qiyu Sun
This paper presents a Carleman-Fourier linearization method for nonlinear dynamical systems with periodic vector fields involving multiple fundamental frequencies. By employing Fou…