Various closeness results in discretized bifurcations
type: Item
instance of: scholarly article
title: Various closeness results in discretized bifurcations
zbMATH Open document ID: 1259.65203
author: Joseph Páez Chávez
author: Lajos Lóczi
published in: Differential Equations and Dynamical Systems
publication date: 2012-11-30T00:00:00Z
review text: The authors are mainly concerned with the effect of one-step discretization schemes on the local bifurcation diagrams of dynamical systems around their bifurcation points. They carry out a review of the existing rich literature devoted to this subject. Moreover, they extend some well established results, including their own, concerning the closeness in various bifurcating equilibria of arbitrary codimension. In fact, they show that a ``\(p\)-th order discretization method approximates dynamical objects with an error of order \(p\)''.
Mathematics Subject Classification ID: 65P30
Mathematics Subject Classification ID: 37G10
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 37M20
Mathematics Subject Classification ID: 65L06
zbMATH DE Number: 6111601
zbMATH Keywords: ordinary differential equations
zbMATH Keywords: one-step methods
zbMATH Keywords: Runge-Kutta methods
zbMATH Keywords: topological conjugacy
zbMATH Keywords: numerical continuation
zbMATH Keywords: local bifurcation diagrams
zbMATH Keywords: dynamical systems
reviewed by: Calin Ioan Gheorghiu
MaRDI profile type: Publication
full work available at URL: s12591-012-0135-5
OpenAlex ID: W2103040616
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DOI: 10.1007/S12591-012-0135-5
description: scientific article; zbMATH DE number 6111601