Period-m Motions and Bifurcation Trees in a Periodically Excited, Quadratic Nonlinear Oscillator

DOI10.5890/DNC.2013.08.004zbMath1305.34055OpenAlexW2328059447MaRDI QIDQ2923057

Albert C. J. Luo, Bo Yu

Publication date: 15 October 2014

Published in: The interdisciplinary journal of Discontinuity, Nonlinearity, and Complexity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.5890/dnc.2013.08.004

zbMATH Keywords

Hopf bifurcationnonlinear dynamical systemsquadratic nonlinear oscillatorbifurcation treesgeneralized harmonic balanced methodperiod-\(m\)-motions

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Nonlinear ordinary differential equations and systems (34A34) Bifurcation theory for ordinary differential equations (34C23) Forced motions for nonlinear problems in mechanics (70K40) Bifurcations and instability for nonlinear problems in mechanics (70K50) Nonlinear oscillations and coupled oscillators for ordinary differential equations (34C15) Bifurcations of limit cycles and periodic orbits in dynamical systems (37G15) Dynamical systems in classical and celestial mechanics (37N05)

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Analytical solutions of periodic motions in 1-dimensional nonlinear systems ⋮ Bifurcation Trees of Period-1 Motions to Chaos in a Two-Degree-of-Freedom, Nonlinear Oscillator

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