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.

在多卷轴混沌吸引子家族中，我们有多重折叠环面混沌吸引子。如何在实现过程中控制、合并、拆分或修改这些多重环面吸引子的整体或部分，同时保持相同的电路图和相同的微分方程组，引起了应用科学家的关注。在本文中，我们努力通过使用分段过程来解决这些问题，即将分形-分数和经典导数组成的分段导数应用于修改后的多折叠环面系统。该过程中还使用了修改后的分段线性奇数函数。修改后的模型首先通过小波方法进行了数值求解，并进行了数值模拟。结果显示初始多折叠环面吸引子逐渐转变为拉伸或缩小的多折叠环面吸引子。然而，系统的混沌状态通过分段修改得以保留。