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- W4313309664 abstract "A parametrically excited Liénard system is investigated by an asymptotic perturbation (AP) method based on Fourier expansion and time rescaling. This chapter considers the Liénard oscillator in the case of parametric excitation. It uses the AP method to calculate an approximate analytic solution. The chapter derives a model system of two coupled differential equations in the phase and amplitude of solutions. It then performs a global analysis of the model system by the Poincarè–Bendixson theorem, the Dulac's criterion, and energy considerations. The chapter also demonstrates the presence of an unusual infinite-period homoclinic bifurcation. The AP method can be considered as a technique that links together the most useful characteristics of the harmonic balancing and the multiple scales method, but its origin can be found in the theory of weakly nonlinear partial differential equations." @default.
- W4313309664 created "2023-01-06" @default.
- W4313309664 date "2022-12-30" @default.
- W4313309664 modified "2023-09-28" @default.
- W4313309664 title "The Asymptotic Perturbation Method for Remarkable Nonlinear Systems" @default.
- W4313309664 doi "https://doi.org/10.1002/9783527841745.ch2" @default.
- W4313309664 hasPublicationYear "2022" @default.
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