A comparative study of computation of Lyapunov spectra with different algorithms

In this paper we make a detailed numerical comparison between three algorithms for the computation of the full Lyapunov spectrum as well as the associated eigenvectors of general dynamical systems. They are: (a) the standard method, (b) a differential formulation of the standard method, and (c) a new algorithm which does not require rescaling and reorthogonalization. We also bring out the relations among these methods. Moreover, we give a simplified formulation of the new algorithm when the dimensionality of the system is 4. We find that there is reasonable agreement among the Lyapunov spectra obtained using the three algorithms in most cases. However the standard method seems to be the most efficient followed by the new method and the differential version of the standard method (in that order), as far as the CPU time for the computation of the Lyapunov spectra is concerned. The new method is hardly suitable for finding the eigenvectors, whereas the other procedures give nearly identical numerical results.