Detection of Bifurcation Structures by Higher-Order Averaging for Duffing's Equation |
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Authors: | Yagasaki K |
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Institution: | (1) Department of Mechanical and Systems Engineering, Gifu University, Gifu, Gifu, 501-1193, Japan |
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Abstract: | 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. |
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Keywords: | Averaging Duffing equation bifurcation resonance |
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