F. Grond and H.H. Diebner:
Local Lyapunov exponents for dissipative continuous systems. (pdf)
Chaos, Solitons & Fractals 23, 1809-1817 (2005).
We analyze a recently proposed algorithm for computing Lyapunov exponents focusing on its capability to calculate reliable local values for chaotic attractors. The averaging process of local contributions to the global measure becomes interpretable, i.e. they are related to the local topological structure in phase space. We compare the algorithm with the commonly used Wolf algorithm by means of analyzing correlations between coordinates of the chaotic attractor and local values of the Lyapunov exponents. The correlations for the new algorithm turn out to be significantly stronger than those for the Wolf algorithm. Since the usage of scalar measures to capture complex structures can be questioned we discuss these entities along with a more phenomenological description of the scatter plots.
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).
H.H. Diebner and F. Grond: Usability of Synchronization for Cognitive Modeling. (pdf) Chaos, Solitons & Fractals 25, 905-910 (2005).