Asymmetric Duffing oscillator: jump manifold and border set

TL;DR

This paper investigates the jump phenomenon in the forced asymmetric Duffing oscillator by computing the jump manifold, providing insights into the global behavior of possible jumps in the system.

Contribution

It introduces the computation of the jump manifold for the asymmetric Duffing oscillator, revealing global jump behavior not previously characterized.

Findings

Computed the jump manifold for the asymmetric Duffing oscillator

Identified global information about all possible jumps

Enhanced understanding of the system's bifurcation structure

Abstract

We study the jump phenomenon present in the forced asymmetric Duffing oscillator using the known steady-state asymptotic solution. The major result is the computation of the jump manifold, which encodes global information about all possible jumps.