Matlab code for Lyapunov exponents of fractional order systems

Marius-F. Danca, Nikolay Kuznetsov

Full text: http://dx.doi.org/10.1142/S0218127418500670

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Abstract

In this paper the Benettin-Wolf algorithm to determine all Lyapunov exponents for a class offractional-order systems modeled by Caputo's derivative and the corresponding Matlab codeare presented. First it is proved that the considered class of fractional-order systems admitsthe necessary variational system necessary to find the Lyapunov exponents. The underlying nu-merical method to solve the extended system of fractional order, composed of the initial valueproblem and the variational system, is the predictor-corrector Adams-Bashforth-Moulton forfractional differential equations. The Matlab program prints and plots the Lyapunov exponentsas function of time. Also, the programs to obtain Lyapunov exponents as function of the bifur-cation parameter and as function of the fractional order are described. The Matlab program forLyapunov exponents is developed from an existing Matlab program for Lyapunov exponents ofinteger order. To decrease the computing time, a fast Matlab program which implements theAdams-Bashforth-Moulton method, is utilized. Four representative examples are considered.

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