Existence and stability of bifurcating tori in a neighborhood of an equilibrium position
type: Item
instance of: scholarly article
title: Existence and stability of bifurcating tori in a neighborhood of an equilibrium position
zbMATH Open document ID: 0728.34056
DOI: 10.1016/0022-247X(91)90018-U
published in: Journal of Mathematical Analysis and Applications
publication date: 1991-01-01T00:00:00Z
review text: The existence and stability of cycles and twodimensional tori bifurcating from the origin at an Hopf-Hopf-mode interaction with irrational frequency ratio is investigated. By normal form theory the system is reduced to two amplitude equations which are further simplified by coordinate changes. The stability of the bifurcating branches can be determined from the nonlinear parts at the critical parameter value. The procedure is demonstrated for examples with degenerate nonlinear terms.
Mathematics Subject Classification ID: 34D35
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34C15
Mathematics Subject Classification ID: 34C20
zbMATH DE Number: 4202770
zbMATH Keywords: existence and stability of cycles
zbMATH Keywords: twodimensional tori
zbMATH Keywords: Hopf-Hopf-mode interaction with irrational frequency ratio
zbMATH Keywords: normal form theory
author: S. R. Bernfeld
MaRDI profile type: Publication
cites work: Q5529796
cites work: Q5580482
cites work: Sulla stabilita dell'equilibrio nei casi critici
cites work: Q4086092
description: scientific article; zbMATH DE number 4202770