Unstable and Stable Period-m Motions in a Twin-well Potential Duffing Oscillator

DOI10.5890/DNC.2012.03.001zbMath1300.34080OpenAlexW2325589530MaRDI QIDQ5408990

Zianzhe Hang, Albert C. J. Luo

Publication date: 11 April 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.2012.03.001

zbMATH Keywords

Hopf bifurcationDuffing oscillatornonlinear dynamical systemsgeneralized harmonic balance methodperiod-\(m\) motions

Mathematics Subject Classification ID

Periodic solutions to ordinary differential equations (34C25) Theoretical approximation of solutions to ordinary differential equations (34A45) 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) Numerical bifurcation problems (65P30)

Related Items (12)

Numerical scheme for period-\(m\) motion of second-order nonlinear dynamical systems based on generalized harmonic balance method ⋮ Symmetric and asymmetric period-1 motions in a periodically forced, time-delayed, hardening Duffing oscillator ⋮ Approximate Analytical Solutions of A Nonlinear Oscillator Equation Modeling A Constrained Mechanical System ⋮ Analytical solutions of periodic motions in 1-dimensional nonlinear systems ⋮ An analytical method for analyzing symmetry-breaking bifurcation and period-doubling bifurcation ⋮ Analytical Predictions of Period-1 motions to Chaos in a Periodically Driven Quadratic Nonlinear Oscillator with a Time-delay ⋮ Period-1 Evolutions to Chaos in a Periodically Forced Brusselator ⋮ On complex periodic motions and bifurcations in a periodically forced, damped, hardening Duffing oscillator ⋮ Bifurcation trees of period-3 motions to chaos in a time-delayed Duffing oscillator ⋮ Multiple bifurcation trees of period-1 motions to chaos in a periodically forced, time-delayed, hardening Duffing oscillator ⋮ Bifurcation Trees of Period-1 Motions to Chaos in a Two-Degree-of-Freedom, Nonlinear Oscillator ⋮ Periodic Motions to Chaos in Pendulum

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