Symmetries in Hidden Bifurcation Routes to Multiscroll Chaotic Attractors Generated by Saturated Function Series
Résumé
In this paper, hidden bifurcation routes to multiscroll chaotic attractors generated
by saturated function series are explored. The method to find such hidden bifurcation routes
(HBR) depending upon two parameters is similar to the method introduced by Menacer, et al.
(2016) for Chua multiscroll attractors. These HBR are characterized by the maximal range
extension (MARE) of their attractors and coding the appearance order of the scrolls under the
control of the two parameters. Moreover, these HDR have interesting symmetries with respect to
the two parameters. The novelty that this article introduces, is firstly the paradigm of MARE and
the formula giving their approximate value depending upon parameters p and q, which is linked
to the size of the scrolls; secondly the coding of the HBR which is dened for the rst time in-
cluding the basic cell ; and thirdly unearthing the symmetries of these routes, allowing to obtain
their coding without any numerical computation.
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