Bifurcation solutions of resonant cases of nonlinear Mathieu equations
type: Item
instance of: scholarly article
title: Bifurcation solutions of resonant cases of nonlinear Mathieu equations
zbMATH Open document ID: 0736.34036
author: Lintao Mei
author: Yushu Chen
published in: Science in China. Series A
publication date: 1992-06-25T00:00:00Z
review text: The nonlinear Mathieu equation is investigated close to resonance. Using Lyapunov-Schmidt reduction the bifurcation solutions including the main resonance, subharmonic, superharmonic and fractal resonance are studied. A stratification of the parameter space into six regions of topologically equivalent response diagrams is given. This analysis covers many interesting models, among them the Mathieu van der Pol equation, the Mathieu-Duffing equation and the pendulum with vertically vibrating support.
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 70K28
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 13390
zbMATH Keywords: nonlinear Mathieu equation
zbMATH Keywords: Lyapunov-Schmidt reduction
zbMATH Keywords: bifurcation solutions
zbMATH Keywords: main resonance
zbMATH Keywords: subharmonic, superharmonic and fractal resonance
zbMATH Keywords: Mathieu van der Pol equation
zbMATH Keywords: Mathieu-Duffing equation
zbMATH Keywords: pendulum with vertically vibrating support
reviewed by: Alois Steindl
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 13390