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 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 where is the kth Lyapunov exponent in descending order and we show through examples how the method is implemented. It extends many previous results.