Periodic solutions and invariant torus in the Rössler System
arXiv:1903.02398 · doi:10.1088/1361-6544/ab8bae
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.