Study of a degenerate Bogdanov-Takens bifurcation in a family of mechanical oscillators
type: Item
instance of: scholarly article
title: Study of a degenerate Bogdanov-Takens bifurcation in a family of mechanical oscillators
zbMATH Open document ID: 0968.70019
DOI: 10.1016/S0093-6413(98)00040-8
author: A. J. Rondríguez-Luis
author: Emilio Freire Macías
author: Estanislao Gamero
published in: Mechanics Research Communications
publication date: 2001-09-05T00:00:00Z
review text: The authors study nonlinear second-order ordinary differential equations as models of generalized oscillators, and detect periodic behaviour by analysing the bifurcations in these oscillators. The most degenerate equilibria are considered, and a useful information is given about nontrivial oscillatory behaviours and their transitions. In particular, it is shown that a family of mechanical oscillators exhibits a codimension-3 degeneracy associated with a double-zero eigenvalue. The authors claim that their results point out some mistakes in previous papers.
Mathematics Subject Classification ID: 70K50
zbMATH DE Number: 1445938
zbMATH Keywords: nonlinear oscillators
zbMATH Keywords: bifurcations
zbMATH Keywords: nonlinear second-order ordinary differential equations
zbMATH Keywords: generalized oscillators
zbMATH Keywords: periodic behaviour
zbMATH Keywords: degenerate equilibria
zbMATH Keywords: codimension-3 degeneracy
zbMATH Keywords: double-zero eigenvalue
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1445938