Multistability Emergence through Fractional-Order-Derivatives in a PWL Multi-Scroll System
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...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-05-01
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| Series: | Electronics |
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| Online Access: | https://www.mdpi.com/2079-9292/9/6/880 |
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| author | José Luis Echenausía-Monroy Guillermo Huerta-Cuellar Rider Jaimes-Reátegui Juan Hugo García-López Vicente Aboites Bahia Betzavet Cassal-Quiroga Héctor Eduardo Gilardi-Velázquez |
| author_facet | José Luis Echenausía-Monroy Guillermo Huerta-Cuellar Rider Jaimes-Reátegui Juan Hugo García-López Vicente Aboites Bahia Betzavet Cassal-Quiroga Héctor Eduardo Gilardi-Velázquez |
| author_sort | José Luis Echenausía-Monroy |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-03-10T19:34:44Z |
| format | Article |
| id | doaj.art-713b6bef635a4c719d7c27487e8b5f28 |
| institution | Directory Open Access Journal |
| issn | 2079-9292 |
| language | English |
| last_indexed | 2024-03-10T19:34:44Z |
| publishDate | 2020-05-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Electronics |
| spelling | doaj.art-713b6bef635a4c719d7c27487e8b5f282023-11-20T01:47:43ZengMDPI AGElectronics2079-92922020-05-019688010.3390/electronics9060880Multistability Emergence through Fractional-Order-Derivatives in a PWL Multi-Scroll SystemJosé Luis Echenausía-Monroy0Guillermo Huerta-Cuellar1Rider Jaimes-Reátegui2Juan Hugo García-López3Vicente Aboites4Bahia Betzavet Cassal-Quiroga5Héctor Eduardo Gilardi-Velázquez6Dynamical Systems Laboratory, CULagos, Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique Díaz de León 1144, Paseos de la Montaña, Lagos de Moreno 47460, MexicoDynamical Systems Laboratory, CULagos, Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique Díaz de León 1144, Paseos de la Montaña, Lagos de Moreno 47460, MexicoDynamical Systems Laboratory, CULagos, Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique Díaz de León 1144, Paseos de la Montaña, Lagos de Moreno 47460, MexicoDynamical Systems Laboratory, CULagos, Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique Díaz de León 1144, Paseos de la Montaña, Lagos de Moreno 47460, MexicoCentro de Investigaciones en Óptica, CIO, Loma del Bosque 115, Col. Campestre, León 37150, MexicoApplied Mathematics Division, Instituto Potosino de Investigación Científica y Tecnológica, IPICYT, Camino a la Presa San José 2055, Col. Lomas 4ta. Sección, San Luis Potosí 78216, MexicoDynamical Systems Laboratory, CULagos, Universidad de Guadalajara, Centro Universitario de los Lagos, Enrique Díaz de León 1144, Paseos de la Montaña, Lagos de Moreno 47460, MexicoIn 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.https://www.mdpi.com/2079-9292/9/6/880multistabilityfractional-order-derivativesmulti-scroll systemhybrid systemsnon-linear systemsunstable dissipative systems |
| spellingShingle | José Luis Echenausía-Monroy Guillermo Huerta-Cuellar Rider Jaimes-Reátegui Juan Hugo García-López Vicente Aboites Bahia Betzavet Cassal-Quiroga Héctor Eduardo Gilardi-Velázquez Multistability Emergence through Fractional-Order-Derivatives in a PWL Multi-Scroll System Electronics multistability fractional-order-derivatives multi-scroll system hybrid systems non-linear systems unstable dissipative systems |
| title | Multistability Emergence through Fractional-Order-Derivatives in a PWL Multi-Scroll System |
| title_full | Multistability Emergence through Fractional-Order-Derivatives in a PWL Multi-Scroll System |
| title_fullStr | Multistability Emergence through Fractional-Order-Derivatives in a PWL Multi-Scroll System |
| title_full_unstemmed | Multistability Emergence through Fractional-Order-Derivatives in a PWL Multi-Scroll System |
| title_short | Multistability Emergence through Fractional-Order-Derivatives in a PWL Multi-Scroll System |
| title_sort | multistability emergence through fractional order derivatives in a pwl multi scroll system |
| topic | multistability fractional-order-derivatives multi-scroll system hybrid systems non-linear systems unstable dissipative systems |
| url | https://www.mdpi.com/2079-9292/9/6/880 |
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