KAM theorem with large perturbation and application to network of Duffing oscillators

2021/04/13 by Xiaoping Yuan, Lu Chen, Yuan, Xiaoping +3 · 1 citation
Biochemistry, Genetics and Molecular Biology · Physics and Astronomy · #Chaos control and synchronization #Dynamical Systems (math.DS) #FOS: Mathematics #Protein Structure and Dynamics #Quantum chaos and dynamical systems

paper · pdf · doi:10.48550/arxiv.2104.05898

openalex publication_date 2021/04/13 · openalex created_date 2021/04/26 · openalex updated_date 2026/07/28

Abstract

We prove that there is an invariant torus with given Diophantine frequency vector for a class of Hamiltonian systems defined by an integrable large Hamiltonian function with a large non-autonomous Hamiltonian perturbation. As for application, we prove that a finite network of Duffing oscillators with periodic exterior forces possesses Lagrangian stability for almost all initial data.

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