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Detection of Bifurcation Structures by High-Order Averaging for Duffing's Equation

K. Yagasaki
Journal / Anthology

Nonlinear Dynamics
Year: 1999
Volume: 18
Page range: 129-158

Applying the higher-order averaging method, we study the periodically forced, standard Duffing oscillator. A package of the computer algebra system, Mathematica, recently developed by the author and a coworker, is improved and used to implement the tedious but necessary computations for application of higher-order averaging. We detect many types of subharmonic, superharmonic and ultra-subharmonic motions and their bifurcations. A theoretical exposition for a previous numerical observation of a superstructure of bifurcation sets is partly given. A numerical example is also presented and the theoretical predictions are compared with the corresponding simulation results.

*Mathematics > Calculus and Analysis > Differential Equations
*Mathematics > Calculus and Analysis > Harmonic Analysis