In this paper, the emergence of multistable behavior through the use of fractional-order- derivatives in a Piece-Wise Linear (PWL) multi-scroll generator is presented. Using the integration- order as a bifurcation parameter, the stability in the system is modified in such a form that produces a basin of attraction segmentation, creating many stable states as scrolls are generated in the integer-order system. The results here presented reproduce the same phenomenon reported in systems with integer-order derivatives, where the multistable regimen is obtained through a parameter variation. The multistable behavior reported is also validated through electronic simulation. The presented results are not only applicable in engineering fields, but they also enrich the analysis and the understanding of the implications of using fractional integration orders, boosting the development of further and better studies.

中文翻译：

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PWL多滚动系统中通过分数阶导数的多稳定性出现

在本文中，通过在分段明智线性（PWL）多滚动发生器中使用分数阶导数，介绍了多稳态行为的出现。使用积分阶作为分叉参数，系统的稳定性以产生吸引力分割盆地的形式修改，随着整数阶系统中产生滚动而创建许多稳定状态。此处呈现的结果再现了在具有整数阶导数的系统中报告的相同现象，在该系统中，通过参数变化获得多稳态方案。报告的多稳态行为也可以通过电子仿真进行验证。提出的结果不仅适用于工程领域，