No Chaos in Dixon's system
Co-author(s): Matthias Seiß
Reference: International Journal of Bifurcation and Chaos, 31 (2021) 2150044
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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