F Grond, HH Diebner, S Sahle, A Mathias, S Fischer and OE Rossler:
A robust, locally interpretable algorithm for Lyapunov exponents. (pdf)
Chaos, Solitons & Fractals Chaos 16, 841-852 (2003).
Abstract:
An enhanced version of the well known Wolf algorithm for the estimation of the Lyapunov characteristic exponents (LCE) is proposed. It permits interpretation of the local behavior of nonlinear flows. The new variant allows for reliable calculation of the non-uniformity-factors (NUFs). The NUFs can be interpreted as standard deviations of the LCEs. Since the latters can also be estimated by the Wolf algorithm, however, without local information on the flow, the new version ensures local interpretability and therefore allows the calculation of the NUFs. The local contributions to the LCEs which we call "local LCEs" can at least be calculated up to three dimensions. Application of the modified method to a hyperchaotic flow in four dimensions shows that an extension to many dimensions is possible and promises new insight into sofar not fully understood high-dimensional nonlinear systems.
H.H. Diebner and F. Grond: Usability of Synchronization for Cognitive Modeling. (pdf) Chaos, Solitons & Fractals 25, 905-910 (2005).
A robust, locally interpretable algorithm for Lyapunov exponents. (pdf)
Chaos, Solitons & Fractals Chaos 16, 841-852 (2003).
Abstract:
An enhanced version of the well known Wolf algorithm for the estimation of the Lyapunov characteristic exponents (LCE) is proposed. It permits interpretation of the local behavior of nonlinear flows. The new variant allows for reliable calculation of the non-uniformity-factors (NUFs). The NUFs can be interpreted as standard deviations of the LCEs. Since the latters can also be estimated by the Wolf algorithm, however, without local information on the flow, the new version ensures local interpretability and therefore allows the calculation of the NUFs. The local contributions to the LCEs which we call "local LCEs" can at least be calculated up to three dimensions. Application of the modified method to a hyperchaotic flow in four dimensions shows that an extension to many dimensions is possible and promises new insight into sofar not fully understood high-dimensional nonlinear systems.
Related publications:
F. Grond and H.H. Diebner: Local Lyapunov exponents for dissipative continuous systems. (pdf) Chaos, Solitons & Fractals 23, 1809-1817 (2005).H.H. Diebner and F. Grond: Usability of Synchronization for Cognitive Modeling. (pdf) Chaos, Solitons & Fractals 25, 905-910 (2005).