Multispiral Chaos

M. A. Aziz Alaoui
Depart. of Math., Labo. LM, Le Havre University

Proc. IEEE, Control of Oscillations and Chaos, Vol. 1, 88-91, (2000)


In this paper, we give piecewise linear (PWL) versions of dynamical systems such as Duffing equations. Then, by modifying the piecewise-linear function, various `multispiral' strange attractors are shown. These attractors appear as a result of the combination of several `one-spiral' attractors similar to Rossler's or similar to Chua's double scroll. This is demonstrated by some numerical results describing how the dynamic changes and gives rise to `multispiral-attractor' as the number of segments of the piecewise-linearity increases. Bifurcation phenomena and transition from order to `multispiral-chaos' are studied.

Interest and applications: for example in,
1) CNNs (Cellular Neural Networks): using weak linear coupling between chaotic cells, hyperchaos was obtained in a CNN array, this was demonstrated with the n-multispiral hypercube CNN, using n-multispiral as cells. (see the refs therin this paper).
2) secure communications: as the chaos is enhanced in such multispiral attractors, the latter could be used for communicating with chaos for increasing security when transmitting a useful inforamtion.

Ref: M.A. Aziz Alaoui, Rev. Mar. Sc. Phys. 1, 109-125, (1998)

Ref: M.A. Aziz Alaoui, Annales de l'ENIT -medélisation et calcul-, Vol.12(2) (1999)

Ref: M.A. Aziz Alaoui, Int. Journ. of Bifurcation and Chaos 9(6), 1009-1039, (1999)

Fig. 1. An example of amultispiral attractor with 21 spirals for modified Chua's circuit, generated by Eq.(2). See also a multispiral gallery and a multifold gallery.


A GIF animated view of this attractor is (asap) available.

Back to the previous page

Back to Aziz Alaoui's home page