Estimation of Large-Scale Dimension Densities
- We propose a technique to calculate large-scale dimension densities in both higher-dimensional spatio-temporal systems and low-dimensional systems from only a few data points, where known methods usually have an unsatisfactory scaling behavior. This is mainly due to boundary and finite size effects. With our rather simple method we normalize boundary effects and get a significant correction of the dimension estimate. This straightforward approach is basing on rather general assumptions. So even weak coherent structures obtained from small spatial couplings can be detected with this method, what is impossible by using the Lyapunov-dimension density. We demonstrate the efficiency of our technique for coupled logistic maps, coupled tent maps, the Lorenz-attractor and the Roessler-attractor.
Author details: | Corinna Raab, Jürgen KurthsORCiDGND |
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Publication type: | Article |
Language: | English |
Year of first publication: | 2001 |
Publication year: | 2001 |
Release date: | 2017/03/24 |
Source: | Physical Review / E. - 64 (2001), 1, art no. 016216-1 - 016216-5 |
Organizational units: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik und Astronomie |
Institution name at the time of the publication: | Mathematisch-Naturwissenschaftliche Fakultät / Institut für Physik |