Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
Matlab Code for Lyapunov Exponents of Fractional-Order Systems. / Danca, Marius F.; Kuznetsov, Nikolay.
в: International Journal of Bifurcation and Chaos, Том 28, № 5, 1850067, 01.05.2018.Результаты исследований: Научные публикации в периодических изданиях › статья › Рецензирование
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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