Computer Assisted 'Proof' of the Global Existence of Periodic Orbits in the Rössler System

• DOI: 10.48550/arxiv.1408.3397
• Publication Date: 2014-01-01
• Authors: A. E. Botha; W. Dednam
• Keywords: Periodic orbits; Computer-assisted proof; Shooting method; Orbit (dynamics)

The numerical optimized shooting method for finding periodic orbits in nonlinear dynamical systems was employed to determine the existence of well-known R\"ossler system. By optimizing period $T$ and three system parameters, $a$, $b$ $c$, simultaneously, it found that, any initial condition $(x_0,y_0,z_0) \in \Re^3$, there exists at least one set parameters corresponding a orbit passing through $ (x_0,y_0,z_0)$. After discussion this result concluded that its analytical proof may present an interesting new mathematical challenge.