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

Abstract

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 Rössler 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.

6 pages, 1 figure

References in corpus (1)

• On the complete integrability and linearization of nonlinear ordinary differential equations - Part III: Coupled first order equations