Christophe LETELLIER
06/12/2014

Aziz Alaoui

**Aziz Alaoui**

Double-scroll attractors were known sinceone was proposed by Otto Rössler [1] or the Chua circuit was designed but it is possible to produce a larger number of scrolls. This was completed for the first time, at least for the non-autonomous case, by Aziz Alaoui in 1999 [2]. Among other systems he proposed, we here present the one as follows

where

which produces a genus-5 multispiral attractor as shown in Fig. 1 for parameter values

The attractor is here shown in the - plane projection. Its topological analysis is provided in [3].

**Fig. 1. The genus-5 multiscroll attractor.**

[1] **O. E. Rössler**, Continuous chaos,. In : Haken H, editor. *Synergetics*, Proceedings of the international workshop on synergetics at
schloss Elmau (Bavaria, 2–7 May 1977). Springer-Verlag, pp. 184-197, 1977.

[2] **M. A. Aziz-Alaoui**, Differential equations with multispiral attractors, *International Journal of Bifurcation & Chaos*, **9**, 1009-1039, 1999.

[3] **M. Rosalie & C. Letellier**, Toward a general procedure for extracting templates from chaotic attractors bounded by high genus torus, *International Journal of Bifurcation & Chaos*, **24** (4), 1450045, 2014.