Hyperchaos in the generalized Rössler system
- 1 November 1997
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review E
- Vol. 56 (5), 5069-5082
- https://doi.org/10.1103/physreve.56.5069
Abstract
Introduced as a model for hyperchaos, the generalized Rössler system of dimension is obtained by linearly coupling additional degrees of freedom to the original Rössler equation. Under variation of a single control parameter, it is able to exhibit the chaotic hierarchy ranging from fixed points via limit cycles and tori to chaotic and, finally, hyperchaotic attractors. Through the help of a mode transformation, we reveal a structural symmetry of the generalized Rössler system. The latter will allow us to interpret the number, shape, and location in phase space of the observed coexisting attractors within a common scheme for arbitrary odd dimension The appearance of hyperchaos is explained in terms of interacting coexisting attractors. In a second part, we investigate the Lyapunov spectra and related properties of the generalized Rössler system as a function of the dimension We find scaling properties which are not similar to those found in homogeneous, spatially extended systems, indicating that the high-dimensional chaotic dynamics of the generalized Rössler system fundamentally differs from spatiotemporal chaos. If the time scale is chosen properly, though, a universal scaling function of the Lyapunov exponents is found, which is related to the real part of the eigenvalues of an unstable fixed point.
Keywords
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