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

被引：22

作者：

Echenausia-Monroy, Jose Luis ^{[1
]}

Huerta-Cuellar, Guillermo ^{[1
,2
]}

Jaimes-Reategui, Rider ^{[1
]}

Garcia-Lopez, Juan Hugo ^{[1
]}

Aboites, Vicente ^{[3
]}

Cassal-Quiroga, Bahia Betzavet ^{[2
,4
]}

Gilardi-Velazquez, Hector Eduardo ^{[1
,4
]}

机构：

[1] Univ Guadalajara, Dynam Syst Lab, CULagos, Ctr Univ Lagos, Enrique Diaz de Leon 1144, Paseos De La Montana 47460, Lagos De Moreno, Mexico

[2] IPICYT, Div Appl Math, Inst Potosino Invest Cient & Tecnol, Camino Presa San Jose 2055,Col Lomas 4ta Secc, San Luis Potosi 78216, San Luis Potosi, Mexico

[3] Ctr Invest Opt CIO, Loma del Bosque 115, Col Campestre 37150, Leon, Mexico

[4] Univ Panamer, Fac Ingn, Josemaria Escriva de Balaguer 101, Aguascalientes 20290, Aguascalientes, Mexico

来源：

ELECTRONICS | 2020年 / 9卷 / 06期

基金：

芬兰科学院;

关键词：

multistability; fractional-order-derivatives; multi-scroll system; hybrid systems; non-linear systems; unstable dissipative systems; CANONICAL-FORMS; CHAOTIC SYSTEM; IMPLEMENTATION; ATTRACTORS; DESIGN;

D O I：

10.3390/electronics9060880

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

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.

引用

页数：14

共 43 条

[11] CANONICAL FORMS FOR IDENTIFICATION OF MULTIVARIABLE LINEAR-SYSTEMS [J].

DENHAM, MJ .

IEEE TRANSACTIONS ON AUTOMATIC CONTROL, 1974, AC19 (06) :646-656

[12] A predictor-corrector approach for the numerical solution of fractional differential equations [J].

Diethelm, K ;

Ford, NJ ;

Freed, AD .

NONLINEAR DYNAMICS, 2002, 29 (1-4) :3-22

[13] Analysis of Fractional Differential Equations: An Application-Oriented Exposition Using Differential Operators of Caputo Type [J].

Diethelm, Kai .

ANALYSIS OF FRACTIONAL DIFFERENTIAL EQUATIONS: AN APPLICATION-ORIENTED EXPOSITION USING DIFFERENTIAL OPERATORS OF CAPUTO TYPE, 2010, 2004 :3-+

[14] A novel approach to generate attractors with a high number of scrolls [J].

Echenausia-Monroy, J. L. ;

Huerta-Cuellar, G. .

NONLINEAR ANALYSIS-HYBRID SYSTEMS, 2020, 35

[15] Family of Bistable Attractors Contained in an Unstable Dissipative Switching System Associated to a SNLF [J].

Echenausia-Monroy, J. L. ;

Garcia-Lopez, J. H. ;

Jaimes-Reategui, R. ;

Lopez-Mancilla, D. ;

Huerta-Cuellar, G. .

COMPLEXITY, 2018,

[16] Fractional-Order Circuits and Systems: An Emerging Interdisciplinary Research Area [J].

Elwakil, Ahmed S. .

IEEE CIRCUITS AND SYSTEMS MAGAZINE, 2010, 10 (04) :40-50

[17] A class of Chua-like systems with only two saddle-foci of different type [J].

Escalante-Gonzalez, R. J. ;

Gilardi-Velazquez, H. E. ;

Campos-Canton, E. .

IFAC PAPERSONLINE, 2018, 51 (33) :156-161

[18] Measurement of Supercapacitor Fractional-Order Model Parameters From Voltage-Excited Step Response [J].

Freeborn, Todd J. ;

Maundy, Brent ;

Elwakil, Ahmed S. .

IEEE JOURNAL ON EMERGING AND SELECTED TOPICS IN CIRCUITS AND SYSTEMS, 2013, 3 (03) :367-376

[19] Nonclassical point of view of the Brownian motion generation via fractional deterministic model [J].

Gilardi-Velazquez, H. E. ;

Campos-Canton, E. .

INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2018, 29 (03)

[20] Multistability in Piecewise Linear Systems versus Eigenspectra Variation and Round Function [J].

Gilardi-Velazquez, H. E. ;

Ontanon-Garcia, L. J. ;

Hurtado-Rodriguez, D. G. ;

Campos-Canton, E. .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2017, 27 (09)

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