Matlab Code for Lyapunov Exponents of Fractional-Order Systems

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Matlab Code for Lyapunov Exponents of Fractional-Order Systems. / Danca, Marius F.; Kuznetsov, Nikolay.

In: International Journal of Bifurcation and Chaos, Vol. 28, No. 5, 1850067, 01.05.2018.

Research output: Contribution to journal › Article › peer-review

Author

Danca, Marius F. ; Kuznetsov, Nikolay. / Matlab Code for Lyapunov Exponents of Fractional-Order Systems. In: International Journal of Bifurcation and Chaos. 2018 ; Vol. 28, No. 5.

BibTeX

@article{704a2424554c4d4ab7d3439044590a10,

title = "Matlab Code for Lyapunov Exponents of Fractional-Order Systems",

abstract = "In this paper, the Benettin-Wolf algorithm to determine all Lyapunov exponents for a class of fractional-order systems modeled by Caputo's derivative and the corresponding Matlab code are presented. First, it is proved that the considered class of fractional-order systems admits the necessary variational system necessary to find the Lyapunov exponents. The underlying numerical method to solve the extended system of fractional order, composed of the initial value problem and the variational system, is the predictor-corrector Adams-Bashforth-Moulton for fractional differential equations. The Matlab program prints and plots the Lyapunov exponents as function of time. Also, the programs to obtain Lyapunov exponents as function of the bifurcation parameter and as function of the fractional order are described. The Matlab program for Lyapunov exponents is developed from an existing Matlab program for Lyapunov exponents of integer order. To decrease the computing time, a fast Matlab program which implements the Adams-Bashforth-Moulton method, is utilized. Four representative examples are considered.",

keywords = "Benettin-Wolf algorithm, fractional-order dynamical system, Lyapunov exponents, NUMERICAL-SOLUTION, DYNAMICAL-SYSTEMS, DIMENSION, TIME-SERIES, DIFFERENTIAL-EQUATIONS, STRANGE ATTRACTORS, COMPUTATION, SPECTRA",

author = "Danca, {Marius F.} and Nikolay Kuznetsov",

year = "2018",

month = may,

day = "1",

doi = "10.1142/S0218127418500670",

language = "English",

volume = "28",

journal = "International Journal of Bifurcation and Chaos in Applied Sciences and Engineering",

issn = "0218-1274",

publisher = "WORLD SCIENTIFIC PUBL CO PTE LTD",

number = "5",

}

RIS

TY - JOUR

T1 - Matlab Code for Lyapunov Exponents of Fractional-Order Systems

AU - Danca, Marius F.

AU - Kuznetsov, Nikolay

PY - 2018/5/1

Y1 - 2018/5/1

N2 - In this paper, the Benettin-Wolf algorithm to determine all Lyapunov exponents for a class of fractional-order systems modeled by Caputo's derivative and the corresponding Matlab code are presented. First, it is proved that the considered class of fractional-order systems admits the necessary variational system necessary to find the Lyapunov exponents. The underlying numerical method to solve the extended system of fractional order, composed of the initial value problem and the variational system, is the predictor-corrector Adams-Bashforth-Moulton for fractional differential equations. The Matlab program prints and plots the Lyapunov exponents as function of time. Also, the programs to obtain Lyapunov exponents as function of the bifurcation parameter and as function of the fractional order are described. The Matlab program for Lyapunov exponents is developed from an existing Matlab program for Lyapunov exponents of integer order. To decrease the computing time, a fast Matlab program which implements the Adams-Bashforth-Moulton method, is utilized. Four representative examples are considered.

AB - In this paper, the Benettin-Wolf algorithm to determine all Lyapunov exponents for a class of fractional-order systems modeled by Caputo's derivative and the corresponding Matlab code are presented. First, it is proved that the considered class of fractional-order systems admits the necessary variational system necessary to find the Lyapunov exponents. The underlying numerical method to solve the extended system of fractional order, composed of the initial value problem and the variational system, is the predictor-corrector Adams-Bashforth-Moulton for fractional differential equations. The Matlab program prints and plots the Lyapunov exponents as function of time. Also, the programs to obtain Lyapunov exponents as function of the bifurcation parameter and as function of the fractional order are described. The Matlab program for Lyapunov exponents is developed from an existing Matlab program for Lyapunov exponents of integer order. To decrease the computing time, a fast Matlab program which implements the Adams-Bashforth-Moulton method, is utilized. Four representative examples are considered.

KW - Benettin-Wolf algorithm

KW - fractional-order dynamical system

KW - Lyapunov exponents

KW - NUMERICAL-SOLUTION

KW - DYNAMICAL-SYSTEMS

KW - DIMENSION

KW - TIME-SERIES

KW - DIFFERENTIAL-EQUATIONS

KW - STRANGE ATTRACTORS

KW - COMPUTATION

KW - SPECTRA

UR - http://www.scopus.com/inward/record.url?scp=85047872626&partnerID=8YFLogxK

UR - http://arxiv.org/abs/1804.01143

UR - http://www.mendeley.com/research/matlab-code-lyapunov-exponents-fractional-order-systems

U2 - 10.1142/S0218127418500670

DO - 10.1142/S0218127418500670

M3 - Article

AN - SCOPUS:85047872626

VL - 28

JO - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

JF - International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

SN - 0218-1274

IS - 5

M1 - 1850067

ER -

ID: 35274656