Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization

Freddy Christiansen; Hans Henrik Rugh

doi:10.1088/0951-7715/10/5/004

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arXiv · chao-dyn/9611014

Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization

Freddy Christiansen·Hans Henrik Rugh

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Abstract

We present a straightforward and reliable continuous method for computing the full or a 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 k'th Lyapunov exponent in descending order and we show through examples how the method is implemented. It extends many previous results.

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BibTeX RIS

Freddy Christiansen, Hans Henrik Rugh. 1996-11-25. Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization. https://doi.org/10.1088/0951-7715%2F10%2F5%2F004

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