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

TL;DR

This paper analyzes the complex behavior and metamorphoses of the 1:2 resonance in an asymmetric Duffing oscillator, revealing how it interacts with primary resonance through asymptotic solutions and implicit function analysis.

Contribution

It introduces a detailed analysis of the 1:2 resonance metamorphoses and its interaction with primary resonance in an asymmetric Duffing oscillator using implicit function methods.

Findings

Describes complex metamorphoses of 1:2 resonance

Analyzes interaction between 1:2 and primary resonance

Provides amplitude-frequency implicit solutions

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.