An improved algorithm for Lyapunov exponents of fractional-order system

This paper presents a modified algorithm for Lyapunov spectrum of fractional-order continuous-time system based on the Jacobian method and the C_C method. First, the relationship between the calculation accuracy and step size is revealed by comparing with several other algorithms for the Lorenz system. Then, our new algorithm is applied to the fractional-order Chen system, the fractional-order Lorenz system and the fractional-order hyperchaotic Röllser system, and is also compared with famous Wolf method. The numerical results suggest that the algorithm not only can calculate the whole Lyapunov spectrum at the same time, but also can improve the calculation accuracy. In addition, the performance of this algorithm can be easily improved by implementing on multi-cores processers.