Slow periodic crossing of a pitchfork bifurcation in an oscillating system
type: Item
instance of: scholarly article
title: Slow periodic crossing of a pitchfork bifurcation in an oscillating system
zbMATH Open document ID: 0894.70015
DOI: 10.1023/A:1008247430863
published in: Nonlinear Dynamics
publication date: 1998-09-07T00:00:00Z
review text: The nonlinear Mathieu equation is investigated as a case study of damped oscillating systems with slowly varying forcing function. The phase portrait of the system changes qualitatively with time with a pitchfork bifurcation point involved. A Poincaré map is constructed in order to describe the dynamics of the system as it repeatedly crosses the bifurcation point. The averaging methods and asymptotic matching techniques connecting local solutions are employed. Numerical simulations are compared with maps obtained analytically.
Mathematics Subject Classification ID: 70K50
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37C75
zbMATH DE Number: 1042565
zbMATH Keywords: KAM theorem
zbMATH Keywords: nonlinear Mathieu equation
zbMATH Keywords: damped oscillating systems
zbMATH Keywords: phase portrait
zbMATH Keywords: Poincaré map
zbMATH Keywords: averaging methods
zbMATH Keywords: asymptotic matching
author: G. J. M. Marée
reviewed by: Piotr Garbaczewski
MaRDI profile type: Publication
full work available at URL: a:1008247430863
OpenAlex ID: W52770662
description: scientific article; zbMATH DE number 1042565