When a chaotic attractor is produced by a three-dimensional strongly dissipative system, its ultimate characterization is reached when a branched manifold—a template—can be used to describe the relative organization of the unstable periodic orbits around which it is structured. If topological characterization was completed for many chaotic attractors, the case of toroidal chaos—a chaotic regime based on a toroidal structure—is still challenging. We here investigate the topology of toroidal chaos, first by using an inductive approach, starting from the branched manifold for the Rössler attractor. The driven van der Pol system—in Robert Shaw’s form—is used as a realization of that branched manifold. Then, using a deductive approach, the branched manifold for the chaotic attractor produced by the Deng toroidal system is extracted from data.
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January 2021
Research Article|
January 14 2021
Topological characterization of toroidal chaos: A branched manifold for the Deng toroidal attractor
Special Collection:
Chaos: From Theory to Applications
Sylvain Mangiarotti
;
Sylvain Mangiarotti
a)
1
Centre d’Études Spatiales de la Biosphère, UPS-CNRS-CNES-IRD-INRA, Observatoire Midi-Pyrénées
, 18 avenue Édouard Belin, 31401 Toulouse, France
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Christophe Letellier
Christophe Letellier
b)
2
Rouen Normandie University—CORIA, Campus Universitaire du Madrillet
, F-76800 Saint-Etienne du Rouvray, France
b)Author to whom correspondence should be addressed: christophe.letellier@coria.fr. URL: http://www.atomosyd.net/spip.php?article1
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a)
Electronic mail: sylvain.mangiarotti@ird.fr
b)Author to whom correspondence should be addressed: christophe.letellier@coria.fr. URL: http://www.atomosyd.net/spip.php?article1
Note: This paper is part of the Focus Issue, Chaos: From Theory to Applications.
Chaos 31, 013129 (2021)
Article history
Received:
August 19 2020
Accepted:
December 29 2020
Citation
Sylvain Mangiarotti, Christophe Letellier; Topological characterization of toroidal chaos: A branched manifold for the Deng toroidal attractor. Chaos 1 January 2021; 31 (1): 013129. https://doi.org/10.1063/5.0025924
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