Multistability Emergence through Fractional-Order-Derivatives in a PWL Multi-Scroll System

• Main Authors: José Luis Echenausía-Monroy, Guillermo Huerta-Cuellar, Rider Jaimes-Reátegui, Juan Hugo García-López, Vicente Aboites, Bahia Betzavet Cassal-Quiroga, Héctor Eduardo Gilardi-Velázquez
• Format: Article
• Language: English
• Published: MDPI AG 2020-05-01
• Series: Electronics
• Subjects: multistability; fractional-order-derivatives; multi-scroll system; hybrid systems; non-linear systems; unstable dissipative systems
• Online Access: https://www.mdpi.com/2079-9292/9/6/880

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.