Alternative algorithm for the computation of Lyapunov spectra of dynamical systems

Recently a new method for the computation of Lyapunov exponents that does not require rescaling and reorthogonalization was proposed [Rangarajan, Habib, and Ryne, Phys. Rev. Lett. 80, 3747 (1998)]. In this paper we make a detailed numerical comparison of the new method and a standard algorithm, as regards accuracy and efficiency, by applying them to some typical two-, three-, and four-dimensional systems. We find that in most cases there is reasonable agreement between the Lyapunov spectra obtained using the two algorithms. The CPU times required for computation are also comparable. However, in certain strongly chaotic cases, the new method was found to be either inefficient (taking a lot of CPU time for computation) or inaccurate.