Šil'nikov-Hopf bifurcations
type: Item
instance of: scholarly article
title: Šil'nikov-Hopf bifurcations
zbMATH Open document ID: 0827.34025
author: Bo Deng
author: Kunimochi Sakamoto
published in: Journal of Differential Equations
publication date: 1995-11-26T00:00:00Z
review text: The authors present a numerical bifurcation study of the dynamical behavior of a structural dynamics model of a periodically forced suspended cable. The simplified equations of motion are: \(\ddot x+ \mu \dot x+ c_1 x+ c_2 x^2+ c_3 x^3= P\cos(\Omega t)\); \(c_1\), \(c_2\), \(c_3\) are fixed parameters. One- and two-parameter diagrams of local bifurcation phenomena near the subharmonic 1:2 resonance are computed. Various global bifurcation phenomena near the resonance, including transitions to chaotic oscillations, are exposed by computation of invariant manifolds of saddle cycles.
reviewed by: Abdelkader Boucherif
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 65H17
zbMATH DE Number: 768997
zbMATH Keywords: numerical bifurcation study
zbMATH Keywords: structural dynamics model
zbMATH Keywords: periodically forced suspended cable
zbMATH Keywords: subharmonic 1:2 resonance
zbMATH Keywords: global bifurcation phenomena
zbMATH Keywords: transitions to chaotic oscillations
MaRDI profile type: Publication
full work available at URL: jdeq.1995.1082
OpenAlex ID: W2089890759
DOI: 10.1006/JDEQ.1995.1082
description: scientific article; zbMATH DE number 768997