Bifurcations near 1:2 subharmonic resonance in a structural dynamics model
type: Item
instance of: scholarly article
title: Bifurcations near 1:2 subharmonic resonance in a structural dynamics model
zbMATH Open document ID: 0827.34028
DOI: 10.1016/0960-0779(94)00147-I
author: Yanyan Li
published in: Chaos, Solitons and Fractals
publication date: 1995-07-03T00:00:00Z
review text: The paper deals with the two-parameter family of ordinary differential equations (1) \(\dot u= F(u, \alpha)\), \((u, \alpha)\in \mathbb{R}^d\times \mathbb{R}^2\), \(d\geq 3\), where \(F\) is of class \(C^r\), \(r\geq 4\). The main assumptions are \(u= 0\) is an equilibrium point for all \(\alpha\) in \(\mathbb{R}^2\), and when \(\alpha= 0\) there is a homoclinic solution \(U_0(t)\) of \(u= 0\) and \(u= 0\) undergoes a supercritical Hopf bifurcation. The objective of the paper is to study the generic codimension two bifurcations of such Sil'nikov-Hopf point. Exploiting the center- exponential expansion of Deng, the authors generalize earlier results of Sil'nikov to Hopf points.
reviewed by: Abdelkader Boucherif
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 37G99
Mathematics Subject Classification ID: 54H20
zbMATH DE Number: 770018
zbMATH Keywords: homoclinic solution
zbMATH Keywords: supercritical Hopf bifurcation
zbMATH Keywords: codimension two bifurcations
zbMATH Keywords: Sil'nikov-Hopf point
MaRDI profile type: Publication
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cites work: Bifurcations and chaos in a model of a rolling railway wheelset
cites work: Periodic and chaotic motions of an unsymmetrical oscillator in nonlinear structural dynamics
cites work: Prediction of bifurcations and chaos for an asymmetric elastic oscillator
cites work: Q4040287
cites work: Q4692840
cites work: Interpolants for Runge-Kutta formulas
cites work: Q3993493
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description: scientific article; zbMATH DE number 770018