Quantum mechanics

Control (management)

Chaotic

MATLAB

Applied mathematics

Operating system

Economics

Set (abstract data type)

Computer science

Code (set theory)

Physics

Nonlinear system

Lyapunov equation

Mathematics

Lyapunov exponent

Lyapunov function

Mathematical analysis

Artificial intelligence

Programming language

Finance

Control theory (sociology)

Fractional calculus

Order (exchange)

International Journal of Bifurcation and Chaos

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.

Matlab Code for Lyapunov Exponents of Fractional-Order Systems