Bifurcation of asymptotically stable periodic solutions in nearly impact oscillators

TL;DR

This paper investigates the bifurcation of stable periodic solutions in nearly impact oscillators using an averaging method, addressing a singular perturbation problem where classical theories are insufficient.

Contribution

It introduces a novel averaging approach to analyze bifurcations in impact oscillators with nearly infinite stiffness springs, expanding the theoretical understanding.

Findings

Proves bifurcation of stable periodic solutions in nearly impact oscillators.

Addresses a singularly perturbed problem beyond classical theory.

Provides a framework for analyzing impact oscillators with extreme stiffness.

Abstract

We use an averaging approach to prove bifurcation of asymptotically stable periodic solutions in a bi-linear oscillator whose one spring has nearly infinite stiffness. This leads to a singularly perturbed problem where the classical theory does not apply.