Computer Assisted 'Proof' of the Global Existence of Periodic Orbits in the R\"ossler System

FOS: Physical sciences Chaotic Dynamics (nlin.CD) Nonlinear Sciences - Chaotic Dynamics
DOI: 10.48550/arxiv.1408.3397 Publication Date: 2014-01-01
ABSTRACT
6 pages, 1 figure<br/>The numerical optimized shooting method for finding periodic orbits in nonlinear dynamical systems was employed to determine the existence of periodic orbits in the well-known R��ssler system. By optimizing the period $T$ and the three system parameters, $a$, $b$ and $c$, simultaneously, it was found that, for any initial condition $(x_0,y_0,z_0) \in \Re^3$, there exists at least one set of optimized parameters corresponding to a periodic orbit passing through $ (x_0,y_0,z_0)$. After a discussion of this result it was concluded that its analytical proof may present an interesting new mathematical challenge.<br/>
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