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

Periodic orbits Computer-assisted proof Shooting method Orbit (dynamics)
DOI: 10.48550/arxiv.1408.3397 Publication Date: 2014-01-01
ABSTRACT
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.
SUPPLEMENTAL MATERIAL
Coming soon ....
REFERENCES ()
CITATIONS ()
EXTERNAL LINKS
PlumX Metrics
RECOMMENDATIONS
FAIR ASSESSMENT
Coming soon ....
JUPYTER LAB
Coming soon ....