Types of change of stability and corresponding types of bifurcations
type: Item
instance of: scholarly article
title: Types of change of stability and corresponding types of bifurcations
zbMATH Open document ID: 0986.37042
published in: Discrete and Continuous Dynamical Systems
publication date: 2000-08-16T00:00:00Z
review text: The goal of this paper is to show connections between change of stability and different types of bifurcation. In particular the authors adress the case where an invariant set \(M\) is unstable (for instance of saddle-type) for a certain parameter value \(\lambda_0\), and stable for certain nearby values. Two types of bifurcations are considered: ``extracritical'', that is splitting of the set \(M\) as \(\lambda\) passes the value \(\lambda_0\), and ``critical'', a term which refers to the accumulation of closed invariant sets at \(\lambda= \lambda_0\). Moreover, two kinds of change of stability are considered, corresponding to the presence or absence of a certain generalized equistability property for \(\lambda\neq \lambda_0\).
Mathematics Subject Classification ID: 37G30
Mathematics Subject Classification ID: 37C75
zbMATH DE Number: 1492607
zbMATH Keywords: stability
zbMATH Keywords: bifurcation
zbMATH Keywords: change of stability
zbMATH Keywords: invariant set
author: Luis Antonio Aguirre
author: Peter Seibert
reviewed by: Messoud Efendiev
MaRDI profile type: Publication
full work available at URL: dcds.1999.5.741
OpenAlex ID: W1966154193
DOI: 10.3934/DCDS.1999.5.741
description: scientific article; zbMATH DE number 1492607