Bifurcation Trees of Period-m Motions to Chaos in a Time-Delayed, Quadratic Nonlinear Oscillator under a Periodic Excitation

DOI10.5890/DNC.2014.03.007zbMath1401.70033OpenAlexW2321580082MaRDI QIDQ2922986

Hanxiang Jin, Albert C. J. Luo

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.2014.03.007

zbMATH Keywords

Hopf bifurcationnonlinear dynamical systemsnonlinear oscillatortime-delayedbifurcation treesgeneralized harmonic balanceperiod-\(m\) motions

Mathematics Subject Classification ID

Bifurcations and instability for nonlinear problems in mechanics (70K50) Transition to stochasticity (chaotic behavior) for nonlinear problems in mechanics (70K55)

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Symmetric and asymmetric period-1 motions in a periodically forced, time-delayed, hardening Duffing oscillator ⋮ Analytical Predictions of Period-1 motions to Chaos in a Periodically Driven Quadratic Nonlinear Oscillator with a Time-delay ⋮ Time-Delay Effects on Periodic Motions in a 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 ⋮ A novel Lie-group theory and complexity of nonlinear dynamical systems ⋮ On Periodic Motions in a Time-Delayed, Quadratic Nonlinear Oscillator with Excitation ⋮ On a Global Sequential Scenario of Bifurcation Trees to Chaos in a First-Order, Periodically Excited, Time-Delayed System ⋮ Period-3 motions to chaos in an inverted pendulum with a periodic base movement

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