Quasi-periodic solutions and sub-harmonic bifurcation of Duffing's equations with quasi-periodic perturbation

DOI10.1007/BF02684038zbMath1020.34038MaRDI QIDQ1864220

Zhu-jun Jing, Peng-cheng Xu

Publication date: 17 March 2003

Published in: Acta Mathematicae Applicatae Sinica. English Series (Search for Journal in Brave)

zbMATH Keywords

existencequasi-periodic solutionssub-harmonic bifurcation

Mathematics Subject Classification ID

Bifurcation theory for ordinary differential equations (34C23) Forced motions for nonlinear problems in mechanics (70K40) Quasi-periodic motions and invariant tori for nonlinear problems in mechanics (70K43) Averaging method for ordinary differential equations (34C29) Almost and pseudo-almost periodic solutions to ordinary differential equations (34C27)

Related Items

Bifurcations and chaos in Duffing equation with damping and external excitations ⋮ Complex dynamics in Duffing system with two external forcings ⋮ Resonant motions in the presence of degeneracies for quasi-periodically perturbed systems

Cites Work

• Unnamed Item
• Second-order averaging and chaos in quasiperiodically forced weakly nonlinear oscillators
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• The bifurcation to homoclinic tori in the quasiperiodically forced Duffing oscillator
• Homoclinic Orbits in Slowly Varying Oscillators
• Chaotic Dynamics of a Quasi-Periodically Forced Beam
• Bifurcations and chaos in a quasi-periodically forced beam: theory, simulation and experiment
• Combination tones for Duffing's equation

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