Detection of bifurcation structures by higher-order averaging for Duffing's equation

DOI10.1023/A:1008371723533zbMath0944.70017MaRDI QIDQ1303139

Kazuyuki Yagasaki

Publication date: 20 September 2000

Published in: Nonlinear Dynamics (Search for Journal in Brave)

zbMATH Keywords

resonancecomputer algebra system Mathematicabifurcation setssubharmonic motionshigher-order averaging methodperiodically forced Duffing oscillatorsuperharmonic motionsultra-subharmonic motions

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Bifurcation theory for ordinary differential equations (34C23) Forced motions for nonlinear problems in mechanics (70K40) Bifurcations and instability for nonlinear problems in mechanics (70K50) Averaging of perturbations for nonlinear problems in mechanics (70K65)

Related Items (11)

Bifurcations of periodic orbits in Duffing equation with periodic damping and external excitations ⋮ Bifurcations and chaos in three-well Duffing system with one external forcing ⋮ Self-excited dynamics of an elastically restrained slender rigid body in uniform compressible laminar flow ⋮ Bifurcations and chaos in Duffing equation with damping and external excitations ⋮ Bifurcation of periodic orbits and chaos in Duffing equation ⋮ Families of solitons in Bragg supergratings ⋮ Bifurcations of periodic orbits in three-well Duffing system with a phase shift ⋮ Complex dynamics in three-well Duffing system with two external forcings ⋮ Bifurcations and chaos in Duffing equation ⋮ Complex dynamics in Duffing system with two external forcings ⋮ Complex dynamics in Duffing-Van der Pol equation

Uses Software

• Mathematica
• MACSYMA
• AUTO-86
• Dynamics

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