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No Chaos in Dixon's system
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| Co-author(s): Matthias Seiß |
| Reference: International Journal of Bifurcation and Chaos, 31 (2021) 2150044 (20 pages) |
| Description: We prove rigorously that there is no chaos in Dixon's system by exhibiting a system
with the same trajectories satisfying the assumptions of the Poincare-Bendixson theorem.
The numerical "evidence" of chaos is simply due to existence of two elliptic sectors at
the origin for certain parameter values. Furthermore, we provide a comprehensive
analysis of the parameter dependency of this system. We show that the parameter
space can be divided into 16 different regions on which the system shows a uniform behaviour
(including the behaviour at infinity). |
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