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arXiv · 1903.02398

Periodic solutions and invariant torus in the Rössler System

Murilo R. Cândido·Douglas D. Novaes·Claudia Valls
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Abstract

The Rössler System is characterized by a three-parameter family of quadratic 3D vector fields. There exist two one-parameter families of Rössler Systems exhibiting a zero-Hopf equilibrium. For Rössler Systems near to one of these families, we provide generic conditions ensuring the existence of a torus bifurcation. In this case, the torus surrounds a periodic solution that bifurcates from the zero-Hopf equilibrium. For Rössler Systems near to the other family, we provide generic conditions for the existence of a periodic solution bifurcating from the zero-Hopf equilibrium. This improves currently known results regarding periodic solutions for such a family. In addition, the stability properties of the periodic solutions and invariant torus are analysed.

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Murilo R. Cândido, Douglas D. Novaes, Claudia Valls. 2021-10-07. Periodic solutions and invariant torus in the Rössler System. https://doi.org/10.1088/1361-6544%2Fab8bae

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