Suppression of period doubling in the dynamics of a bouncing ball
type: Item
instance of: scholarly article
title: Suppression of period doubling in the dynamics of a bouncing ball
zbMATH Open document ID: 0612.58034
DOI: 10.1016/0167-2789(87)90232-6
author: Kurt Wiesenfeld
published in: Physica D
publication date: 1987-01-01T00:00:00Z
review text: We present a theoretical and experimental study of a ''bouncing ball'' system, where the effect of a near-resonant perturbation is to suppress the onset of the first period doubling bifurcation. Near the bifurcation point, the full dynamical equations are reduced to a discrete-time map governing the dynamics on a slowly oscillating center manifold. The derivation emphasizes the geometry of the phase-space dynamics, and serves to clarify several points of a recently proposed theory regarding the effects of strong near-resonant perturbations. Our experimental results agree with the simple theory for moderate perturbations; for larger perturbations, higher order effects must be included.
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37B99
zbMATH DE Number: 3990454
zbMATH Keywords: bouncing ball system
zbMATH Keywords: near-resonant perturbation
zbMATH Keywords: period doubling bifurcation
zbMATH Keywords: near-resonant perturbations
MaRDI profile type: Publication
full work available at URL: 0167-2789(87)90232-6
OpenAlex ID: W2076152754
cites work: Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
cites work: Q1233671
cites work: Applications of centre manifold theory
cites work: The dynamics of repeated impacts with a sinusoidally vibrating table
cites work: Chaotic dynamics of a bouncing ball
cites work: Q3893028
cites work: On the Origin of the Cosmic Radiation
description: scientific article; zbMATH DE number 3990454