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Construction of bifurcation diagrams of Van der Pol - Duffing oscillator [Elektronski vir]
Pušenjak, Rudi, 1947- ; Oblak, Maks
The incremental harmonic balance method with multiple time scales is applied to perform parametric studies of steady-state oscillations, which appear in forced van der Pol - Duffing oscillator, ...subjected to the harmonic excitation. Parametric studies in dependence on variable excitation frequency and amplitude are formulated, which enable construction of various bifurcation diagrams. To overcome difficulties in bifurcation points, where the singularity of Jacobian matrix arises, the improved arc-Iength continuationis used. The bifurcation diagram of a hinged-hinged beam under harmonic bending force is studied in details. Periodic and almost periodic oscillations of forced van der Pol-Duffing oscillator are analyzed in the example.
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