On bifurcation into nonresonant quasi-periodic motions
type: Item
instance of: scholarly article
title: On bifurcation into nonresonant quasi-periodic motions
zbMATH Open document ID: 0663.34044
DOI: 10.1016/0307-904X(88)90011-X
published in: Applied Mathematical Modelling
publication date: 1988-01-01T00:00:00Z
review text: Consider the autonomous system \(dz^ i/dt=Z^ i(z^ j;\eta^{\beta})\) where \(z^ i\) are the components of the state vector and the \(\eta^{\beta}\) are parameters. The paper is devoted to the study of the behaviour of the system in the vicinity of a coincident critical point characterized by Jacobian, which has two pairs of pure imaginary eigenvalues and all remaining eigenvalues have negative real parts. The stability, instability, and different types of bifurcation are studied. For simplicity it is assumed that the system is four-dimensional and involves only two independent parameters. An illustrative application to the electrical network is included.
Mathematics Subject Classification ID: 37-XX
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34C27
zbMATH DE Number: 4084113
zbMATH Keywords: autonomous system
zbMATH Keywords: coincident critical point
zbMATH Keywords: eigenvalues
zbMATH Keywords: bifurcation
zbMATH Keywords: application
zbMATH Keywords: electrical network
author: K. Huseyin
author: P. Yu
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4084113