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[63850] Artykuł: Metamorphoses of resonance curves in systems of coupled oscillators: The case of degenerate singular pointsCzasopismo: International Journal of Non-Linear Mechanics Tom: 95, Strony: 272-276ISSN: 0020-7462 Opublikowano: Lipiec 2017 Autorzy / Redaktorzy / Twórcy Grupa MNiSW: Publikacja w czasopismach wymienionych w wykazie ministra MNiSzW (część A) Punkty MNiSW: 30 Pełny tekst DOI Keywords: Coupled oscillators  Metamorphoses of amplitude curves  Degenerate singular points  |
We study dynamics of two coupled periodically driven oscillators. The internal motion is separated off exactly to yield a nonlinear fourth-order equation describing inner dynamics. Periodic steady-state solutions of the fourth-order equation are determined within the Krylov–Bogoliubov–Mitropolsky approach and we compute the corresponding amplitude profiles.
Metamorphoses of these amplitude curves induced by changes of control parameters as well as the corresponding changes of dynamics are studied within the framework of theory of differential properties of algebraic curves. The major finding is that there is a very rich dynamics in eighborhoods of degenerate singular points.