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.

accepted

References in corpus (11)

• Practical implementation of nonlinear time series methods: The TISEAN package
• The Lyapunov Characteristic Exponents and their computation
• A comparative study of computation of Lyapunov spectra with different algorithms
• Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system
• Differences and similarities in the analysis of Lorenz, Chen, and Lu systems
• Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization
• Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations
• The Lyapunov dimension formula for the global attractor of the Lorenz system
• Hidden transient chaotic attractors of Rabinovich-Fabrikant system
• Complex dynamics, hidden attractors and continuous approximation of a fractional-order hyperchaotic PWC system
• An Extension of the Well-Posedness Concept for Fractional Differential Equations of Caputo's Type

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