Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization

Details Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization Computing Lyapunov spectra with continuous Gram-Schmidt orthonormalization

1996-11-25

arxiv.org/abs/chao-dyn/9611014v1

Nonlinear Sciences

Chaotic Dynamics

14 pages, 10 PS figures, ioplppt.sty, iopl12.sty, epsfig.sty 44 kB

Scientific paper

10.1088/0951-7715/10/5/004

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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