Difference equations versus differential equations, a possible equivalence for the Rössler system?
type: Item
instance of: scholarly article
title: Difference equations versus differential equations, a possible equivalence for the Rössler system?
zbMATH Open document ID: 1056.39023
author: C. Letellier
author: Aziz Alaoui
author: Saber Elaydi
author: Luis Antonio Aguirre
published in: Physica D
publication date: 2004-11-12T00:00:00Z
full work available at URL: https://digitalcommons.trinity.edu/cgi/viewcontent.cgi
review text: The authors discuss the possible equivalence between ordinary differential equations and difference equations which are obtained by discretization. First the paper deals with the Rössler system, several simulations about the discrete equation are obtained which explain the evolution of the dynamics. The authors establish that the solutions of the discrete equation are topologically equivalent to the solutions of the Rössler system as long as the the time step must be less than the threshold value associated with the Nyquist criterion. Then it is proved that the discretisation of two nonlinear ordinary differential can exhibit a chaotic regime. The dynamics of solutions depend on the discretization time step of each ordinary differential equation. To illustrate this result, several numerical simulations are given.
Mathematics Subject Classification ID: 39A12
Mathematics Subject Classification ID: 34C28
Mathematics Subject Classification ID: 37D45
Mathematics Subject Classification ID: 65L05
zbMATH DE Number: 2115237
zbMATH Keywords: nonlinear dynamical systems
zbMATH Keywords: Rössler system
zbMATH Keywords: time discretization
zbMATH Keywords: Nyquist criterion
zbMATH Keywords: numerical instabilities
zbMATH Keywords: global modelling.
reviewed by: Khalil Ezzinbi
MaRDI profile type: Publication
OpenAlex ID: W2062703100
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DOI: 10.1016/J.PHYSD.2004.02.007
description: scientific article; zbMATH DE number 2115237