IMPLEMENTATION OF MULTI-FOLDED TORUS ATTRACTORS VIA A PIECEWISE SYSTEM WITH A PIECEWISE LINEAR ODD FUNCTION

Abstract

Among the family of multi-scroll chaotic attractors, we have the multi-folded torus chaotic attractor. Concerns were raised among applied scientists on how to control, merge, split or modify the whole or parts of these multi-folded torus attractors in their implementation processes while conserving the same circuit diagram and the same system of differential equations. In this paper, we strive to address these concerns by using the piecewise process, that is, applying to the modified multi-folded torus system, the piecewise derivative made of the fractal-fractional and classical derivatives. A modified piecewise linear odd function is also used in the process. The modified model is first solved numerically thanks to the wavelet method and numerical simulations are performed. The results show the progressive transformation of the initial multi-folded torus attractors into stretched or reduced multi-folded torus attractors. However, the chaotic state of the system is preserved by the piecewise modification.