2020/07/21 by Murilo R Cândido, Douglas D Novaes, Claudia Valls · 1 citation
Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Chaos control and synchronization #Nonlinear Differential Equations Analysis
paper · doi:10.1088/1361-6544/ab8bae
openalex created_date 2019/03/22 · openalex publication_date 2020/07/21 · openalex updated_date 2026/07/30
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.