Asymmetric Duffing oscillator: metamorphoses of 1:2 resonance and its interaction with the primary resonance

2024/07/03 by Kyziol, Jan, Okniński, Andrzej
#37G35 #37M20 #Chaotic Dynamics (nlin.CD) #FOS: Physical sciences

paper · doi:10.48550/arxiv.2407.03423

Abstract

We investigate the 1: 2 resonance in the periodically forced asymmetric Duffing oscillator due to the period-doubling of the primary 1: 1 resonance or forming independently, coexisting with the primary resonance. We compute the steady-state asymptotic solution - the amplitude-frequency implicit function. Working in the differential properties of implicit functions framework, we describe complicated metamorphoses of the 1:2 resonance and its interaction with the primary resonance.

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