Templates of Two Foliated Attractors — Lorenz and Chen Systems

Abstract

A chaotic attractor solution of the Lorenz system [Lorenz, 1963] with foliated structure is topologically characterized. Its template permits to both summarize the organization of its periodic orbits and detail the topology of the solution as a branched manifold. A template of an attractor solution of the Chen system [Chen & Ueta, 1999] with a similar foliated structure is also established.

Chaotic mechanism description by an elementary mixer for the template of an attractor

“…Here we give some references where the authors give the templates of attractors bounded by genus one torus: Rössler attractors by Letellier et al [16], Duffing oscillator attractor by Gilmore & McCallum [17], Burke-Shaw attractor by Letellier et al [18] and recently we propose the template of Malasoma attractors [10,14]. This method can also be applied to attractors bounded by torus with an higher genus mainly by Letellier & co-workers, for instance, it is the case for templates of the Lorenz attractors [19], Chen attractor [20], Chua attractors [21] and multiscroll attractor [22].…”