Periodic solutions and invariant torus in the R\"ossler System
Abstract
The R\"ossler System is characterized by a three-parameter family of quadratic 3D vector fields. There exist two one-parameter families of R\"ossler Systems exhibiting a zero-Hopf equilibrium. For R\"ossler 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 R\"ossler 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.
Keywords
Cite
@article{arxiv.1903.02398,
title = {Periodic solutions and invariant torus in the R\"ossler System},
author = {Murilo R. Cândido and Douglas D. Novaes and Claudia Valls},
journal= {arXiv preprint arXiv:1903.02398},
year = {2021}
}