Mangiarotti Sylvain, Letellier Christophe
Centre d'Études Spatiales de la Biosphère, UPS-CNRS-CNES-IRD-INRA, Observatoire Midi-Pyrénées, 18 avenue Édouard Belin, 31401 Toulouse, France.
Rouen Normandie University-CORIA, Campus Universitaire du Madrillet, F-76800 Saint-Etienne du Rouvray, France.
Chaos. 2021 Jan;31(1):013129. doi: 10.1063/5.0025924.
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.
当一个三维强耗散系统产生一个混沌吸引子时，当一个分支流形——一个模板——可用于描述其周围不稳定周期轨道的相对组织时，就达到了对其最终的表征。如果对许多混沌吸引子完成了拓扑表征，那么环形混沌（一种基于环形结构的混沌状态）的情况仍然具有挑战性。我们在此研究环形混沌的拓扑结构，首先采用归纳法，从罗斯勒吸引子的分支流形入手。以罗伯特·肖的形式表示的受驱范德波尔系统被用作该分支流形的一种实现。然后，采用演绎法，从数据中提取邓环形系统产生的混沌吸引子的分支流形。
