Journal article
Poincare sections for a new three-dimensional toroidal attractor
Journal of physics. A, Mathematical and theoretical, v 42(1), pp 015101-015101 (16)
09 Jan 2009
Abstract
A new 3D autonomous dynamical system proposed by Li (2008 Phys. Lett. A 372 387) produces a chaotic attractor whose global topological properties are unusual. The attractor has a rotation symmetry and only a single real fixed point for the parameters used in his study. The symmetric, complex pair of fixed points cannot be ignored: they play a major role in organizing the motion on a surface of peculiar toroidal type. We describe this attractor, propose a simple, intuitive model to understand it, show that it is of toroidal type and of genus three, construct a global Poincare surface of section with two disjoint components and use this section to locate unstable periodic orbits and determine their topological period. We also show that its image attractor is of genus one and supports flow on a simple wrinkled torus. Finally, we use the interplay between the original covering attractor and its image as an aid to understand why the Li attractor is of genus-three type.
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Details
- Title
- Poincare sections for a new three-dimensional toroidal attractor
- Creators
- Christophe Letellier - University of RouenRobert Gilmore - Drexel University
- Publication Details
- Journal of physics. A, Mathematical and theoretical, v 42(1), pp 015101-015101 (16)
- Publisher
- Iop Publishing Ltd
- Number of pages
- 16
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- [Retired Faculty]
- Web of Science ID
- WOS:000261397900009
- Scopus ID
- 2-s2.0-64549116234
- Other Identifier
- 991019167996404721
InCites Highlights
Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- International collaboration
- Web of Science research areas
- Physics, Mathematical
- Physics, Multidisciplinary