Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization

We present a straightforward and reliable continuous method for computing the full or partial Lyapunov spectrum associated with a dynamical system specified by a set of differential-equations. We do this by introducing a stability parameter beta > 0 and augmenting the dynamical system with an orthonormal k-dimensional frame and a Lyapunov vector such that the frame is continuously Gram-Schmidt orthonormalized and at most linear growth of the dynamical variables is involved. We prove that the method is strongly stable when beta > -lambda(k) where lambda(k) is the kth Lyapunov exponent in descending order and we show through examples how the method is implemented. It extends many previous results.