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[142520] Artykuł: The Duffing Oscillator: Metamorphoses of 1 : 2 Resonance and Its Interaction with the Primary ResonanceCzasopismo: Nonlinear Dynamics and Systems Theory Tom: 25, Zeszyt: 5, Strony: 535-545ISSN: 1562-8353 Opublikowano: Pażdziernik 2025 Liczba arkuszy wydawniczych: 2.00 Autorzy / Redaktorzy / Twórcy Grupa MNiSW: Publikacja w czasopismach wymienionych w wykazie ministra MNiSzW (część A) Punkty MNiSW: 40 Keywords: Duffing equation  resonances  singularities  metamorphoses.  |
We investigate the 1 : 2 resonance in the periodically forced asymmetric Duffing oscillator, it is created via the period-doubling of the primary 1 : 1 resonance or forming independently and coexisting with the primary resonance. We compute the steady-state asymptotic solution – the amplitude-frequency response function. Working in the framework of differential properties of implicit functions, we discover and describe complicated metamorphoses of the 1 : 2 resonance and its interaction with the primary resonance.