The coupled 1:2 resonance in a symmetric case and parametric amplification model

DOI10.3934/dcdsb.2020255zbMath1471.37060OpenAlexW3083482083MaRDI QIDQ2033764

Reza Mazrooei-Sebdani, Zahra Yousefi

Publication date: 17 June 2021

Published in: Discrete and Continuous Dynamical Systems. Series B (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/dcdsb.2020255

zbMATH Keywords

symmetryoptimizationrelative equilibrianormal formsfirst integralsmaximumcoupled Hamiltonian 1:2 resonancefour wave mixing model

Mathematics Subject Classification ID

Hamilton's equations (70H05) Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests (37J35) Perturbations of finite-dimensional Hamiltonian systems, normal forms, small divisors, KAM theory, Arnol'd diffusion (37J40) Completely integrable systems and methods of integration for problems in Hamiltonian and Lagrangian mechanics (70H06) Nonlinear resonances for nonlinear problems in mechanics (70K30)

Related Items (6)

Periodic Klein-Gordon chains with three particles in 1:2:2 resonance ⋮ Hamiltonian Hopf bifurcations near a chaotic Hamiltonian resonance ⋮ On the integrability of twofold 1 : 2 Hamiltonian resonance ⋮ On detuned 1:1:3 Hamiltonian resonance with cases of symmetric cubic and quartic potentials ⋮ Nondegenerate Hamiltonian Hopf bifurcations in \(\omega:3:6\) resonance \((\omega=1\) or \(2)\) ⋮ All relative equilibria of Hamiltonian in detuned 1:2:3 resonance

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