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

José Luis Echenausía-Monroy; Guillermo Huerta-Cuellar; Rider Jaimes-Reátegui; Juan Hugo García-López; Vicente Aboites; Cassal Quiroga, Bahia Betzavet; Gilardi Velázquez, Héctor Eduardo

doi:10.3390/electronics9060880

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

Journal

Electronics

ISSN

2079-9292

Date Issued

2020

Author(s)

José Luis Echenausía-Monroy

Guillermo Huerta-Cuellar

Rider Jaimes-Reátegui

Juan Hugo García-López

Vicente Aboites

Cassal Quiroga, Bahia Betzavet

Facultad de Ingeniería - CampAGS

Gilardi Velázquez, Héctor Eduardo

Facultad de Ingeniería - CampAGS

Type

text::journal::journal article

DOI

10.3390/electronics9060880

URL

https://scripta.up.edu.mx/handle/20.500.12552/3172

Abstract

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.