Computation of Lyapunov characteristic exponents for continuous dynamical systems

Abstract

A new method for computing all the Lyapunov characteristic exponents (LCEs) of n-dimensional continuous dynamical systems is presented. The method relies on the use of the Cayley Transform and a development of the ability to restart the computations for the variational equation. The method intrinsically maintains the orthogonality of the Q matrix in the QR decomposition of the solution of the variational equation. It therefore does not suffer from the type of computational breakdown that occurs with the standard method for computing LCEs. An example of a Lorenz system showing the breakdown of the standard method is presented, and the same example is used to compute the LCEs by the present method. Comparisons of the computational efficiency of the proposed method in relation to the standard method, and the standard-method-with-reorthogonalization are presented. Issues of accuracy are addressed.