Discretization of non-Lipschitz continuous O.D.E. and chaos
type: Item
instance of: scholarly article
title: Discretization of non-Lipschitz continuous O.D.E. and chaos
zbMATH Open document ID: 0858.65077
author: Yoichi Maeda
author: Masaya Yamaguti
published in: Proceedings of the Japan Academy. Series A
publication date: 1997-03-25T00:00:00Z
review text: This article considers scalar autonomous ordinary differential equations with only one stable equilibrium point. It presents necessary and sufficient conditions under which the explicit Euler discretization is stable in a neighborhood of the equilibrium point. Furthermore, it gives sufficient conditions under which the Euler discretization has periodic orbits with period 2, and sufficient conditions under which it is chaotic.
reviewed by: Ernst Hairer
Mathematics Subject Classification ID: 65L07
Mathematics Subject Classification ID: 65L05
Mathematics Subject Classification ID: 65L06
Mathematics Subject Classification ID: 34A34
Mathematics Subject Classification ID: 65L20
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 37G99
zbMATH DE Number: 938075
zbMATH Keywords: chaos
zbMATH Keywords: autonomous ordinary differential equations
zbMATH Keywords: stable equilibrium point
zbMATH Keywords: explicit Euler discretization
zbMATH Keywords: periodic orbits
MaRDI profile type: Publication
full work available at URL: pjaa.72.43
OpenAlex ID: W2003446881
cites work: Euler's discretization revisited
cites work: Period Three Implies Chaos
cites work: Q4362436
DOI: 10.3792/PJAA.72.43
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description: scientific article; zbMATH DE number 938075