Preprint
No Chaos in Dixon's System
Zusammenfassung
The so-called Dixon system is often cited as an example of a two-dimensional (continuous) dynamical system that exhibits chaotic behaviour, if its two parameters take their value in a certain domain. We provide first a rigorous proof that there is no chaos in Dixon's system. Then we perform a complete bifurcation analysis of the system showing that the parameter space can be decomposed into sixteen different regions in each of which the system exhibits qualitatively the same behaviour. In particular, we prove that in some regions two elliptic sectors with infinitely many homoclinic orbits exist which can easily create in numerical computations the impression of chaotic behaviour.
Zitieren
@article{doi:10.17170/kobra-202002161006,
author={Seiler, Werner M. and Seiß, Matthias},
title={No Chaos in Dixon's System},
year={2020}
}
0500 Oax 0501 Text $btxt$2rdacontent 0502 Computermedien $bc$2rdacarrier 1100 2020$n2020 1500 1/eng 2050 ##0##http://hdl.handle.net/123456789/11470 3000 Seiler, Werner M. 3010 Seiß, Matthias 4000 No Chaos in Dixon's System / Seiler, Werner M. 4030 4060 Online-Ressource 4085 ##0##=u http://nbn-resolving.de/http://hdl.handle.net/123456789/11470=x R 4204 \$dPreprint 4170 Mathematische Schriften Kassel ;; [2020, 01] 7136 ##0##http://hdl.handle.net/123456789/11470
2020-03-06T09:56:21Z 2020-03-06T09:56:21Z 2020 doi:10.17170/kobra-202002161006 http://hdl.handle.net/123456789/11470 eng Namensnennung-NichtKommerziell-KeineBearbeitung 3.0 Deutschland http://creativecommons.org/licenses/by-nc-nd/3.0/de/ Dixon´s system singularity blow-up homoclinic orbits chaos 510 No Chaos in Dixon's System Preprint The so-called Dixon system is often cited as an example of a two-dimensional (continuous) dynamical system that exhibits chaotic behaviour, if its two parameters take their value in a certain domain. We provide first a rigorous proof that there is no chaos in Dixon's system. Then we perform a complete bifurcation analysis of the system showing that the parameter space can be decomposed into sixteen different regions in each of which the system exhibits qualitatively the same behaviour. In particular, we prove that in some regions two elliptic sectors with infinitely many homoclinic orbits exist which can easily create in numerical computations the impression of chaotic behaviour. open access Seiler, Werner M. Seiß, Matthias 21 Seiten Mathematische Schriften Kassel ;; [2020, 01] Kassel, Universität Kassel, Fachbereich Mathematik und Naturwissenschaften, Institut für Mathematik submittedVersion Mathematische Schriften Kassel [2020, 01] false
Die folgenden Lizenzbestimmungen sind mit dieser Ressource verbunden: