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- Title
No Chaos in Dixon's System.
- Authors
Seiler, Werner M.; Seiß, Matthias
- Abstract
The so-called Dixon system is often cited as an example of a two-dimensional (continuous) dynamical system that exhibits chaotic behavior, if its two parameters take their values 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 16 different regions in each of which the system exhibits qualitatively the same behavior. In particular, we prove that in some regions two elliptic sectors with infinitely many homoclinic orbits exist.
- Subjects
DYNAMICAL systems; ELLIPTICAL orbits
- Publication
International Journal of Bifurcation & Chaos in Applied Sciences & Engineering, 2021, Vol 31, Issue 3, pN.PAG
- ISSN
0218-1274
- Publication type
Article
- DOI
10.1142/S0218127421500449